Probability - Aptitude Questions and Answers - Wikitechy https://www.wikitechy.com/interview-questions/tag/probability-aptitude-questions-and-answers/ Interview Questions Mon, 06 Sep 2021 06:45:06 +0000 en-US hourly 1 https://wordpress.org/?v=6.9 https://www.wikitechy.com/interview-questions/wp-content/uploads/2025/10/cropped-wikitechy-icon-32x32.png Probability - Aptitude Questions and Answers - Wikitechy https://www.wikitechy.com/interview-questions/tag/probability-aptitude-questions-and-answers/ 32 32 A brother and sister appear for an interview against two vacant posts in an office. The probability of the brother’s selection is 1/5th and that of the sister’s selections is 1/3rd. What is the probability that one of them is selected ? https://www.wikitechy.com/interview-questions/probability/a-brother-and-sister-appear-for-an-interview-against-two-vacant-posts-in-an-office-the-probability-of-the-brothers-selection-is-1-5th-and-that-of-the-sisters-selections-is-1-3rd-what-is-the-prob/ https://www.wikitechy.com/interview-questions/probability/a-brother-and-sister-appear-for-an-interview-against-two-vacant-posts-in-an-office-the-probability-of-the-brothers-selection-is-1-5th-and-that-of-the-sisters-selections-is-1-3rd-what-is-the-prob/#respond Wed, 18 Aug 2021 02:10:04 +0000 https://www.wikitechy.com/interview-questions/?p=2051

A brother and sister appear for an interview against two vacant posts in an office. The probability of the brother’s selection is 1/5th and that of the sister’s selections is 1/3rd. What is the probability that one of them is selected ?

A. 1/5

B. 2/5

C. 1/3

D. 2/3

Answer : B. 2/5

Explanation:

Probability that only one of them is selected = (prob. that brother is selected) × (prob. that sister is not selected) + (Prob. that brother is not selected) × (Prob. that sister is selected)

Hence, Required Probability = 1/5 x 2/3 + 4/5 x 1/3
= 2/15 + 4/15
= 6/15
= 2/5.

]]> https://www.wikitechy.com/interview-questions/probability/a-brother-and-sister-appear-for-an-interview-against-two-vacant-posts-in-an-office-the-probability-of-the-brothers-selection-is-1-5th-and-that-of-the-sisters-selections-is-1-3rd-what-is-the-prob/feed/ 0 A bag contains 8 red and 5 white balls. 2 balls are drawn at random. What is the probability that both are white ? https://www.wikitechy.com/interview-questions/probability/a-bag-contains-8-red-and-5-white-balls-2-balls-are-drawn-at-random-what-is-the-probability-that-both-are-white/ https://www.wikitechy.com/interview-questions/probability/a-bag-contains-8-red-and-5-white-balls-2-balls-are-drawn-at-random-what-is-the-probability-that-both-are-white/#respond Wed, 18 Aug 2021 02:08:13 +0000 https://www.wikitechy.com/interview-questions/?p=2050

A bag contains 8 red and 5 white balls. 2 balls are drawn at random. What is the probability that both are white ?

A. 5/16

B. 2/13

C. 3/26

D. 5/39

Answer : D. 5/39

Explanation:

  • n(S) = Number of methods for drawing 2 balls out of 13 = 13C2
    = (13 x 12) / 2
    = 78.
  • n(E) = No. of methods for drawing 2 balls out of 5 = 5C2
    = (5 x 4) / 2
    = 10.
  • Therefore, P(E) = n(E) / n(S)
    = 10/78
    = 5/39.
]]> https://www.wikitechy.com/interview-questions/probability/a-bag-contains-8-red-and-5-white-balls-2-balls-are-drawn-at-random-what-is-the-probability-that-both-are-white/feed/ 0 Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5 ? https://www.wikitechy.com/interview-questions/probability/tickets-numbered-1-to-20-are-mixed-up-and-then-a-ticket-is-drawn-at-random-what-is-the-probability-that-the-ticket-drawn-has-a-number-which-is-a-multiple-of-3-or-5/ https://www.wikitechy.com/interview-questions/probability/tickets-numbered-1-to-20-are-mixed-up-and-then-a-ticket-is-drawn-at-random-what-is-the-probability-that-the-ticket-drawn-has-a-number-which-is-a-multiple-of-3-or-5/#respond Wed, 18 Aug 2021 01:48:27 +0000 https://www.wikitechy.com/interview-questions/?p=2032

Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5 ?

A. 1/2

B. 2/5

C. 8/12

D. 9/20

Answer : D. 9/20…

Explanation:

Here, S = {1, 2, 3, 4, 19, 20}.
Let E = event of getting a multiple of 3 or 5
= {3, 6 , 9, 12, 15, 18, 5, 10, 20}.
P(E) = n(E) / n(S)
= 9/20

]]> https://www.wikitechy.com/interview-questions/probability/tickets-numbered-1-to-20-are-mixed-up-and-then-a-ticket-is-drawn-at-random-what-is-the-probability-that-the-ticket-drawn-has-a-number-which-is-a-multiple-of-3-or-5/feed/ 0 A bag contains 4 black, 5 yellow and 6 green balls. Three balls are drawn at random from the bag. What is the probability that all of them are yellow ? https://www.wikitechy.com/interview-questions/probability/a-bag-contains-4-black-5-yellow-and-6-green-balls-three-balls-are-drawn-at-random-from-the-bag-what-is-the-probability-that-all-of-them-are-yellow/ https://www.wikitechy.com/interview-questions/probability/a-bag-contains-4-black-5-yellow-and-6-green-balls-three-balls-are-drawn-at-random-from-the-bag-what-is-the-probability-that-all-of-them-are-yellow/#respond Wed, 18 Aug 2021 01:37:06 +0000 https://www.wikitechy.com/interview-questions/?p=2026

A bag contains 4 black, 5 yellow and 6 green balls. Three balls are drawn at random from the bag. What is the probability that all of them are yellow ?

A. 2/91

B. 1/81

C. 1/8

D. 2/81

Answer : A. 2/91

Explanation:

Total number of balls = 4 + 5 + 6 = 15
Let S be the sample space.
n(S) = Total number of ways of drawing 3 balls out of 15 = 15C3
Let E = Event of drawing 3 balls, all of them are yellow.
n(E) = Number of ways of drawing 3 balls, all of them are yellow = Number of ways of drawing 3 balls from the total 5 = 5C3 (∵ there are 5 yellow balls in the total balls)
P(E) = n(E)/n(S) = 2/91

]]> https://www.wikitechy.com/interview-questions/probability/a-bag-contains-4-black-5-yellow-and-6-green-balls-three-balls-are-drawn-at-random-from-the-bag-what-is-the-probability-that-all-of-them-are-yellow/feed/ 0 When two dice are tossed, What is the probability that the total score is a prime number ? https://www.wikitechy.com/interview-questions/probability/when-two-dice-are-tossed-what-is-the-probability-that-the-total-score-is-a-prime-number/ https://www.wikitechy.com/interview-questions/probability/when-two-dice-are-tossed-what-is-the-probability-that-the-total-score-is-a-prime-number/#respond Wed, 18 Aug 2021 01:36:03 +0000 https://www.wikitechy.com/interview-questions/?p=2025

When two dice are tossed, What is the probability that the total score is a prime number ?

A. 1/4

B. 1/3

C. 2/3

D. 5/12

Answer : D. 5/12

Explanation:

Total number of outcomes possible when a die is rolled = 6 (∵ any one face out of the 6 faces).
Hence, Total number of outcomes possible when two dice are rolled, n(S) = 6 × 6 = 36.
Prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 … etc
Let E = the event that the total is a prime number
= {(1,1), (1,2), (1,4), (1,6), (2,1), (2,3), (2,5), (3,2), (3,4), (4,1), (4,3), (5,2), (5,6), (6,1), (6,5)}
Hence, n(E) = 15
P(E) = n(E)/n(S)
= 15/36 = 5/12

]]> https://www.wikitechy.com/interview-questions/probability/when-two-dice-are-tossed-what-is-the-probability-that-the-total-score-is-a-prime-number/feed/ 0