InterviewSolution
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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
Two dice are tossed. The probability that the total score is a prime number is: |
| Answer» Clearly, n(S) = (6 x 6) = 36. Let E = Event that the sum is a prime number. Then E = { (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) } n(E) = 15. P(E) = n(E) = 15 = 5 . n(S) 36 12 | |
| 2. |
In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green? |
| Answer» Total number of balls = (8 + 7 + 6) = 21. Let E = event that the ball drawn is neither red nor green = event that the ball drawn is blue. n(E) = 7. P(E) = n(E) = 7 = 1 . n(S) 21 3 | |
| 3. |
A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue? |
| Answer» Total number of balls = (2 + 3 + 2) = 7. Let S be the sample space. Then, n(S) = Number of ways of drawing 2 balls out of 7 = 7C2 ` = (7 x 6) (2 x 1) = 21. Let E = Event of drawing 2 balls, none of which is blue. n(E) = Number of ways of drawing 2 balls out of (2 + 3) balls. = 5C2 = (5 x 4) (2 x 1) = 10. P(E) = n(E) = 10 . n(S) 21 | |
| 4. |
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? |
| Answer» 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) = 9 . n(S) 20 | |
| 5. |
What is the probability of getting a sum 9 from two throws of a dice? |
| Answer» In two throws of a dice, n(S) = (6 x 6) = 36. Let E = event of getting a sum ={(3, 6), (4, 5), (5, 4), (6, 3)}. P(E) = n(E) = 4 = 1 . n(S) 36 9 | |
| 6. |
Three unbiased coins are tossed. What is the probability of getting at most two heads? |
| Answer» Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH} Let E = event of getting at most two heads. Then E = {TTT, TTH, THT, HTT, THH, HTH, HHT}. P(E) = n(E) = 7 . n(S) 8 | |
| 7. |
In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize? |
| Answer» P (getting a prize) = 10 = 10 = 2 . (10 + 25) 35 7 | |
| 8. |
Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even? |
| Answer» In a simultaneous throw of two dice, we have n(S) = (6 x 6) = 36. Then, E = {(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3, 4), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 4), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)} n(E) = 27. P(E) = n(E) = 27 = 3 . n(S) 36 4 | |
| 9. |
In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected, is: |
| Answer» Let S be the sample space and E be the event of selecting 1 girl and 2 boys. Then, n(S) = Number ways of selecting 3 students out of 25 = 25C3 ` = (25 x 24 x 23) (3 x 2 x 1) = 2300. n(E) = (10C1 x 15C2) = 10 x (15 x 14) (2 x 1) = 1050. P(E) = n(E) = 1050 = 21 . n(S) 2300 46 | |
| 10. |
A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart is: |
| Answer» Here, n(S) = 52. Let E = event of getting a queen of club or a king of heart. Then, n(E) = 2. P(E) = n(E) = 2 = 1 . n(S) 52 26 | |
| 11. |
A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is: |
| Answer» Let S be the sample space. Then, n(S) = number of ways of drawing 3 balls out of 15 = 15C3 = (15 x 14 x 13) (3 x 2 x 1) = 455. Let E = event of getting all the 3 red balls. n(E) = 5C3 = 5C2 = (5 x 4) = 10. (2 x 1) P(E) = n(E) = 10 = 2 . n(S) 455 91 | |
| 12. |
Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart, is: |
| Answer» Let S be the sample space. Then, n(S) = 52C2 = (52 x 51) = 1326. (2 x 1) Let E = event of getting 1 spade and 1 heart. n(E) = number of ways of choosing 1 spade out of 13 and 1 heart out of 13 = (13C1 x 13C1) = (13 x 13) = 169. P(E) = n(E) = 169 = 13 . n(S) 1326 102 | |
| 13. |
A bag contains 6 black and 8 white balls. One ball is drawn at random. What is the probability that the ball drawn is white? |
| Answer» Let number of balls = (6 + 8) = 14. Number of white balls = 8. P (drawing a white ball) = 8 = 4 . 14 7 | |
| 14. |
One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a face card (Jack, Queen and King only)? |
| Answer» Clearly, there are 52 cards, out of which there are 12 face cards. P (getting a face card) = 12 = 3 . 52 13 | |
| 15. |
From a pack of 52 cards, two cards are drawn together at random. What is the probability of both the cards being kings? |
| Answer» Let S be the sample space. Then, n(S) = 52C2 = (52 x 51) = 1326. (2 x 1) Let E = event of getting 2 kings out of 4. n(E) = 4C2 = (4 x 3) = 6. (2 x 1) P(E) = n(E) = 6 = 1 . n(S) 1326 221 | |
| 16. |
A box contains 6 black, 5 brown and 2 yellow balls. If 2 balls are selected at random, what is the probability that both are black?(A) 4/23(B) 5/26(C) 7/26(D) 8/15 |
| Answer» | |
| 17. |
An urn contains 12 red and 18 white marbles. Two marbles are drawn without replacement one after another. What is the probability that first is red and second is white?(A) 16/145(B) 9/32(C) 36/145(D) 5/32 |
| Answer» None | |
| 18. |
4 dices are thrown simultaneously. What is the probability that all the dices show the same number.(A) 1/216(B) 1/36(C) 4/216(D) 4/36 |
| Answer» | |
| 19. |
Ram speaks truth in 3/4 of cases and Shyam in 4/5 of cases. In what percent of cases while narrating the same event are they likely to contradict each other?(A) 35%(B) 25%(C) 20%(D) 40% |
| Answer» | |
| 20. |
A box having 5 black and 3 brown flags. Another box having 4 black and 6 brown flags. If one flag is drawn from each box.Find the probability that both flags are of different color.(A) 21/40(B) 10/19(C) 3/8(D) 3/10 |
| Answer» | |
| 21. |
Given a coin which gives HEADS with probability 1/4 and TAILS with 3/4. The coin is tossed k times. What is the probability that we get at least k/2 HEADS is less than or equal to?(A) (1/2) k/5(B) (1/2) k/2(C) (1/3) k/2(D) (1/5) k/2 |
| Answer» | |