How many possibilities are there in each of the following?<\/strong>
i. Vanita knows the following sites in Maharashtra. She is planning to visit one of them in her summer vacation. Ajintha, Mahabaleshwar, Lonar Sarovar, Tadoba wild life sanctuary, Amboli, Raigad, Matheran, Anandavan.
ii. Any day of a week is to be selected randomly.
iii. Select one card from the pack of 52 cards.
iv. One number from 10 to 20 is written on each card. Select one card randomly.
Solution:
<\/strong>i. Here, 8 sites of Maharashtra are given.
\u2234 There are 8 possibilities in a random experiment of visiting a site out of 8 sites in Maharashtra.<\/p>\n\n\n\n
ii. There are 7 days in a week.
\u2234 There are 7 possibilities in a random experiment of selecting a day of the week.<\/p>\n\n\n\n
iii. There are 52 cards in a pack of cards.
\u2234 There are 52 possibilities in a random experiment of selecting one card from the pack of 52 cards.<\/p>\n\n\n\n
iv. There are 11 cards numbered from 10 to 20.
\u2234 There are 11 possibilities in a random experiment of selecting one card from the given set of cards.<\/p>\n\n\n\n
Question 1. ii. There are two possibilities (H or T) on tossing a coin i.e. 12 possibility. Question 2. Question 1. Question 2. Question 3. Question 4. Question 1. Some examples of finite sample space. (Textbook pg. no, 117) i. One die is rolled, ii. Two dice are rolled simultaneously, iii. Three coins are tossed simultaneously. iv. Two digit numbers are formed using digits 0, 1, 2, 3, 4, 5 without repetition of the digits. v. From three men and two women, environment committee of two persons is to be formed. vi. One coin and one die are thrown simultaneously. ii. Sample space, Condition for event B: The sum of the digits on the upper faces is minimum 10. Condition for event C: The same digit on both the upper faces. iii. Sample space, Condition for event A: To get at least two heads. Condition for event B: To get no head. Condition for event C: To get head on the second coin. iv. Sample space (S) = {10, 12, 13, 14, 15, v. Let the three men be M1<\/sub>, M2<\/sub>, M3<\/sub> and the two women be W1<\/sub>, W2<\/sub>. vi. Sample space, Question 1. i. Let A be the event of getting at least one head. ii. Let B be the event of getting no head. Question 2. i. Let A be the event that the sum of the digits on the upper faces is at least 10. ii. Let B be the event that the sum of the digits on the upper faces is 33. iii. Let C be the event that the digit on the first die is greater than the digit on the second die. Question 3. i. Let A be the event that the ticket drawn shows an even number. ii. Let B be the event that the ticket drawn shows a number which is a multiple of 5. Question 4. ii. Let B be the event that the number formed is a multiple of 5. Question 5. ii. Let B be the event that the card drawn is a spade. Maharashtra Board Solutions for Class 10-Maths (Part 1): Chapter 5- Probability<\/p>\n\n\n\n Download PDF<\/strong>: Maharashtra Board Solutions for Class 10-Maths (Part 1): Chapter 5- Probability PDF<\/a><\/p>\n\n\n\n You can download the Maharashtra State Board Books from the eBalbharti official website, i.e. cart.ebalbharati.in or from this article.<\/p> <\/div> Students can get the Maharashtra Books for primary, secondary, and senior secondary classes from here.\u00a0 You can view or download the\u00a0Maharashtra State Board Books<\/strong>\u00a0from this page or from the official website for free of cost. Students can follow the detailed steps below to visit the official website and download the e-books for all subjects or a specific subject in different mediums. As of now, the MSCERT and Balbharti are responsible for the syllabus and textbooks of Classes 1 to 8, while Classes 9 and 10 are under the Maharashtra State Board of Secondary and Higher Secondary Education (MSBSHSE).<\/p> <\/div> The Maharashtra State Board of Secondary & Higher Secondary Education, conducts the HSC and SSC Examinations in the state of Maharashtra through its\u00a0nine<\/strong>\u00a0Divisional Boards located at Pune, Mumbai, Aurangabad, Nasik, Kolhapur, Amravati, Latur, Nagpur and Ratnagiri.<\/p> <\/div> <\/div>\n\n\n\n The Maharashtra State Board of Secondary and Higher Secondary Education or MSBSHSE (Marathi: \u092e\u0939\u093e\u0930\u093e\u0937\u094d\u091f\u094d\u0930 \u0930\u093e\u091c\u094d\u092f \u092e\u093e\u0927\u094d\u092f\u092e\u093f\u0915 \u0906\u0923\u093f \u0909\u091a\u094d\u091a \u092e\u093e\u0927\u094d\u092f\u092e\u093f\u0915 \u0936\u093f\u0915\u094d\u0937\u0923 \u092e\u0902\u0921\u0933), is an autonomous and statutory body established in 1965<\/strong>. The board was amended in the year 1977 under the provisions of the Maharashtra Act No. 41 of 1965.<\/p>\n\n\n\n The Maharashtra State Board of Secondary & Higher Secondary Education (MSBSHSE), Pune is an independent body of the Maharashtra Government. There are more than 1.4 million students that appear in the examination every year. The Maha State Board conducts the board examination twice a year. This board conducts the examination for SSC and HSC. <\/p>\n\n\n\n The Maharashtra government established the Maharashtra State Bureau of Textbook Production and Curriculum Research, also commonly referred to as Ebalbharati, in 1967 to take up the responsibility of providing quality textbooks to students from all classes studying under the Maharashtra State Board. MSBHSE prepares and updates the curriculum to provide holistic development for students. It is designed to tackle the difficulty in understanding the concepts with simple language with simple illustrations. Every year around 10 lakh students are enrolled in schools that are affiliated with the Maharashtra State Board.<\/p>\n\n\n\n
In which of the following experiments possibility of expected outcome is more? (Textbook pg, no. 116)<\/strong>
i. Getting 1 on the upper face when a die is thrown.
ii. Getting head by tossing a coin.
Solution:
<\/strong>i. On a die there are 6 numbers.
\u2234 There are 6 possibilities of getting any one number from 1 to 6 on the upper face i.e. 16 is the possibility.<\/p>\n\n\n\n
\u2234 In the second experiment, the possibility of expected outcome is more.<\/p>\n\n\n\n
Throw a die, once. What are the different possibilities of getting dots on the upper face? (Textbook pg. no. 114)
Answer:<\/strong>
There are six different possibilities of getting dots on the upper face. They are![\"Maharashtra](\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/12\/Maharashtra-Board-Class-10-Maths-Solutions-Chapter-5-Probability-Practice-Set-5.1-1-300x52.jpg\")
<\/p>\n\n\n\nPractice Set 5.2<\/h4>\n\n\n\n
For each of the following experiments write sample space \u2018S\u2019 and number of sample Point n(S)
i. One coin and one die are thrown simultaneously.
ii. Two digit numbers are formed using digits 2,3 and 5 without repeating a digit.
Solution:<\/strong>
i. Sample space,
S = {(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6)}
\u2234 n(S) =12
ii. Sample space,
S = {23,25,32, 35, 52, 53}
\u2234 n(S) = 6<\/p>\n\n\n\n
The arrow is rotated and it stops randomly on the disc. Find out on which colour it may stop.<\/strong>![\"Maharashtra](\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/12\/Maharashtra-Board-Class-10-Maths-Solutions-Chapter-5-Probability-Practice-Set-5.2-1.png\")
Solution:
<\/strong>There are total six colours on the disc.
Sample space,
S = {Red, Orange, Yellow, Blue, Green, Purple}
\u2234 n(S) = 6
\u2234 Arrow may stop on any one of the six colours.<\/p>\n\n\n\n
In the month of March 2019, find the days on which the date is a multiple of 5. (see the given page of the calendar).<\/strong>![\"Maharashtra](\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/12\/Maharashtra-Board-Class-10-Maths-Solutions-Chapter-5-Probability-Practice-Set-5.2-2.png\")
Solution:
<\/strong>Dates which are multiple of 5:
5,10, 15,20,25,30
\u2234 S = {Tuesday, Sunday, Friday, Wednesday, Monday, Saturday}
\u2234 n(S) = 6
\u2234 The days on which the date will be a multiple of 5 are Tuesday, Sunday, Friday, Wednesday, Monday and Saturday.<\/p>\n\n\n\n
Form a \u2018Road safety committee\u2019 of two, from 2 boys (B1<\/sub> B2<\/sub>) and 2 girls (G1<\/sub>, G2<\/sub>). Complete the following activity to write the sample space.
Solution:<\/strong>![\"Maharashtra](\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/12\/Maharashtra-Board-Class-10-Maths-Solutions-Chapter-5-Probability-Practice-Set-5.2-3.png\")
<\/p>\n\n\n\n
Sample Space<\/strong><\/p>\n\n\n\n
Solution:<\/strong>![\"Maharashtra](\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/12\/Maharashtra-Board-Class-10-Maths-Solutions-Chapter-5-Probability-Practice-Set-5.2-4.png\")
![\"Maharashtra](\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/12\/Maharashtra-Board-Class-10-Maths-Solutions-Chapter-5-Probability-Practice-Set-5.2-5.png\")
<\/p>\n\n\n\nPractice Set 5.3<\/h4>\n\n\n\n
Event A: Even number on the upper face.
Event B: Odd number on the upper face.
Event C: Prime number on the upper face.<\/p>\n\n\n\n
Event A: The sum of the digits on upper faces is a multiple of 6.
Event B: The sum of the digits on the upper faces is minimum 10.
Event C: The same digit on both the upper faces.<\/p>\n\n\n\n
Condition for event A: To get at least two heads.
Condition for event B: To get no head.
Condition for event C: To get head on the second coin.<\/p>\n\n\n\n
Condition for event A: The number formed is even.
Condition for event B: The number is divisible by 3.
Condition for event C: The number formed is greater than 50.<\/p>\n\n\n\n
Condition for event A: There must be at least one woman member.
Condition for event B: One man, one woman committee to be formed.
Condition for event C: There should not be a woman member.<\/p>\n\n\n\n
Condition for event A: To get head and an odd number.
Condition for event B: To get a head or tail and an even number.
Condition for event C: Number on the upper face is greater than 7 and tail on the coin.
Solution:
<\/strong>i. Sample space (S) = {1, 2, 3, 4, 5, 6}
\u2234 n(S) = 6
Condition for event A: Even number on the upper face.
\u2234 A = {2,4,6}
\u2234 n(A) = 3
Condition for event B: Odd number on the upper face.
\u2234 B = {1, 3, 5}
\u2234 n(B) = 3
Condition for event C: Prime number on the upper face.
\u2234 C = {2, 3, 5}
\u2234 n(C) = 3<\/p>\n\n\n\n
S = {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6),
(2,1), (2,2), (2,3), (2,4), (2,5), (2,6),
(3,1), (3,2), (3,3), (3,4), (3,5), (3,6),
(4,1), (4,2), (4,3), (4,4), (4,5), (4,6),
(5,1), (5,2), (5,3), (5,4), (5,5), (5,6),
(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}
\u2234 n(S) = 36
Condition for event A: The sum of the digits on the upper faces is a multiple of 6.
A = {(1, 5), (2, 4), (3, 3), (4, 2), (5, 1), (6, 6)}
\u2234 n(A) = 6<\/p>\n\n\n\n
B = {(4, 6), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6)}
\u2234 n(B) = 6<\/p>\n\n\n\n
C = {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)}
\u2234 n(C) = 6<\/p>\n\n\n\n
S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}
\u2234 n(S) = 8<\/p>\n\n\n\n
\u2234 A = {HHT, HTH, THH, HHH}
\u2234 n(A) = 4<\/p>\n\n\n\n
\u2234 B = {TTT}
\u2234 n(B) = 1<\/p>\n\n\n\n
\u2234 C = {HHH, HHT, THH, THT}
\u2234 n(C) = 4<\/p>\n\n\n\n
20, 21, 23, 24, 25,
30, 31, 32, 34, 35,
40, 41, 42, 43,
45, 50, 51, 52, 53, 54}
\u2234 n(S) = 25
Condition for event A: The number formed is even
\u2234 A = {10, 12, 14, 20, 24, 30, 32, 34, 40, 42, 50, 52, 54)
\u2234 n(A) = 13
Condition for event B: The number formed is divisible by 3.
\u2234 B = {12, 15, 21, 24, 30, 42, 45, 51, 54}
\u2234 n(B) = 9
Condition for event C: The number formed is greater than 50.
\u2234 C = {51,52, 53,54}
\u2234 n(C) = 4<\/p>\n\n\n\n
Out of these men and women, a environment committee of two persons is to be formed.
\u2234 Sample space,
S = {M1<\/sub>M2<\/sub>, M1<\/sub>M3<\/sub>, M1<\/sub>W1<\/sub>, M1<\/sub>W2<\/sub>, M2<\/sub>M3<\/sub>, M2<\/sub>W1<\/sub>, M2<\/sub>W2<\/sub>, M3<\/sub>W1<\/sub>, M3<\/sub>W2<\/sub>, W1<\/sub>W2<\/sub>}
\u2234 n(S) = 10
Condition for event A: There must be at least one woman member.
\u2234 A = {M1<\/sub>W1<\/sub>, M1<\/sub>W2<\/sub>, M2<\/sub>W1<\/sub>, M2<\/sub>W2<\/sub>, M3<\/sub>W1<\/sub>, M3<\/sub>W2<\/sub>, W1<\/sub>W2<\/sub>}
\u2234 n(A) = 7
Condition for event B: One man, one woman committee to be formed.
\u2234 B = {M1<\/sub>W1<\/sub>, M1<\/sub>W2<\/sub>, M2<\/sub>W1<\/sub>, M2<\/sub>W2<\/sub>, M3<\/sub>W2<\/sub>, M3<\/sub>W2<\/sub>}
\u2234 n(B) = 6
Condition for event C: There should not be a woman member.
\u2234 C = {M1<\/sub>M2<\/sub>, M1<\/sub>M3<\/sub>, M2<\/sub>M3<\/sub>}
\u2234 n(C) = 3<\/p>\n\n\n\n
S = {(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6)}
\u2234 n(S) = 12
Condition for event A: To get head and an odd number.
\u2234 A = {(H, 1), (H, 3), (H, 5)}
\u2234 n(A) = 3
Condition for event B: To get a head or tail and an even number.
\u2234 B = {(H, 2), (H, 4), (H, 6), (T, 2), (T, 4), (T, 6)}
\u2234 n(B) = 6
Condition for event C: Number on the upper face is greater than 7 and tail on the coin.
The greatest number on the upper face of a die is 6.
\u2234 Event C is an impossible event.
\u2234 C = { }
\u2234 n(C) = 0<\/p>\n\n\n\nPractice Set 5.4<\/h4>\n\n\n\n
If two coins are tossed, find the probability of the following events.
i. Getting at least one head.
ii. Getting no head.
Solution:<\/strong>
Sample space,
S = {HH, HT, TH, TT}
\u2234 n(S) = 4<\/p>\n\n\n\n
\u2234 A = {HT, TH, HH}
\u2234 n(A) = 3
\u2234 P(A) = n(A)n(S)
\u2234 P(A) = 34<\/p>\n\n\n\n
\u2234 B = {TT}
\u2234 n(B) = 1
\u2234 P(B) = n(B)n(S)
\u2234 P(B) = 14
\u2234 P(A) = 34; P(B) = 14<\/p>\n\n\n\n
If two dice are rolled simultaneously, find the probability of the following events.
i. The sum of the digits on the upper faces is at least 10.
ii. The sum of the digits on the upper faces is 33.
iii. The digit on the first die is greater than the digit on second die.
Solution:<\/strong>
Sample space,
s = {(1,1), (1,2), (1,3), (1,4), (1, 5), (1,6),
(2, 1), (2, 2), (2,3), (2,4), (2, 5), (2,6),
(3, 1), (3, 2), (3, 3), (3,4), (3, 5), (3, 6),
(4, 1), (4, 2), (4,3), (4,4), (4, 5), (4,6),
(5, 1), (5, 2), (5,3), (5,4), (5, 5), (5, 6),
(6, 1), (6, 2), (6, 3), (6,4), (6, 5), (6,6)}
\u2234 n(S) = 36<\/p>\n\n\n\n
\u2234 A = {(4, 6), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6)}
\u2234 n(A) = 6
\u2234 P(A) = n(A)n(S) = 636
\u2234 P(A) = 16<\/p>\n\n\n\n
The sum of the digits on the upper faces can be maximum 12.
\u2234 Event B is an impossible event.
\u2234 B = { }
\u2234 n(B) = 0
\u2234 P(B) = n(B)n(S) = 036
\u2234 P(B) = 0<\/p>\n\n\n\n
C = {(2, 1), (3, 1), (3,2), (4,1), (4,2), (4, 3), (5, 1), (5,2), (5,3), (5,4), (6,1), (6,2), (6, 3), (6, 4), (6, 5),
\u2234 n(C) = 15
\u2234 P(C) = n(c)n(S) = 1536
\u2234 P(C) = 512
\u2234 P(A) = 16 ; P(B) = 0; P(C) = 512<\/p>\n\n\n\n
There are 15 tickets in a box, each bearing one of the numbers from 1 to 15. One ticket is drawn at random from the box. Find the probability of event that the ticket drawn:
i. shows an even number.
ii. shows a number which is a multiple of 5.
Solution:<\/strong>
Sample space,
S = {1,2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,14, 15}
\u2234 n(S) = 15<\/p>\n\n\n\n
\u2234 A = {2, 4, 6, 8, 10, 12, 14}
\u2234 n(A) = 7
\u2234 P(A) = n(A)n(S)
\u2234 P(A) = 715<\/p>\n\n\n\n
\u2234 B = {5, 10, 15}
\u2234 n(B) = 3
\u2234 P(B) = n(B)n(S) = 315
\u2234 P(B) = 15
\u2234 P(A) = 715 ; P(B) = 15<\/p>\n\n\n\n
A two digit number is formed with digits 2, 3, 5, 7, 9 without repetition. What is the probability that the number formed is
i. an odd number?
ii. a multiple of 5?
Solution:<\/strong>
Sample space
(S) = {23, 25, 27, 29,
32, 35, 37, 39,
52, 53, 57, 59,
72, 73, 75, 79,
92, 93, 95, 97}
\u2234 n(S) = 20
i. Let A be the event that the number formed is an odd number.
\u2234 A = {23, 25, 27, 29, 35, 37, 39, 53, 57, 59, 73, 75,79,93,95,97}
\u2234 n(A) = 16
\u2234 P(A) = n(A)n(S) = 1620
\u2234 P(A) = 45<\/p>\n\n\n\n
\u2234 B = {25,35,75,95}
\u2234 n(B) = 4
\u2234 P(B) = n(B)n(S) = 420
\u2234 P(B) = 15
\u2234 P(A) = 45 ; P(B) = 15<\/p>\n\n\n\n
A card is drawn at random from a pack of well shuffled 52 playing cards. Find the probability that the card drawn is
i. an ace.
ii. a spade.
Solution:<\/strong>
There are 52 playing cards.
\u2234 n(S) = 52
i. Let A be the event that the card drawn is an ace.
\u2234 n(A) = 4
\u2234 P(A) = n(A)n(S) = 452
\u2234 P(A) = 113<\/p>\n\n\n\n
\u2234 n(B) = 13
\u2234 P(B) = n(B)n(S) = 1352
\u2234 P(B) = 14
\u2234 P(A) = 113 ; P(B) = 14<\/p>\n\n\n\nDownload PDF<\/strong><\/h2>\n\n\n\n
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