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- Question
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:
Options- A.
21 46 - B.
25 117 - C.
1 50 - D.
3 25 - Correct Answer
-
21 46
ExplanationLet 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
Probability problems
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- 1. Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?
Options- A.
1 2 - B.
3 4 - C.
3 8 - D.
5 16
Discuss
Correct Answer:3 4
Explanation:
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 - 2. What is the probability of getting a sum 9 from two throws of a dice?
Options- A.
1 6 - B.
1 8 - C.
1 9 - D.
1 12
Discuss
Correct Answer:1 9
Explanation:
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 - 3. A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart is:
Options- A.
1 13 - B.
2 13 - C.
1 26 - D.
1 52
Discuss
Correct Answer:1 26
Explanation:
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 - 4. Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart, is:
Options- A.
3 20 - B.
29 34 - C.
47 100 - D.
13 102
Discuss
Correct Answer:13 102
Explanation:
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 - 5. 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)?
Options- A.
1 13 - B.
3 13 - C.
1 4 - D.
9 52
Discuss
Correct Answer:3 13
Explanation:
Clearly, there are 52 cards, out of which there are 12 face cards.∴ P (getting a face card) = 12 = 3 . 52 13 - 6. From a pack of 52 cards, two cards are drawn together at random. What is the probability of both the cards being kings?
Options- A.
1 15 - B.
25 57 - C.
35 256 - D.
1 221
Discuss
Correct Answer:1 221
Explanation:
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 - 7. 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?
Options- A.
3 4 - B.
4 7 - C.
1 8 - D.
3 7
Discuss
Correct Answer:4 7
Explanation:
Let number of balls = (6 + 8) = 14.Number of white balls = 8.
P (drawing a white ball) = 8 = 4 . 14 7 - 8. 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?
Options- A.
1 3 - B.
3 4 - C.
7 19 - D.
8 21 - E.
9 21
Discuss
Correct Answer:1 3
Explanation:
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 - 9. Three unbiased coins are tossed. What is the probability of getting at most two heads?
Options- A. 3/4
- B. 1/4
- C. 3/8
- D. 7/8 Discuss
Correct Answer: 7/8
Explanation:
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 - 10. 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?
Options- A.
10 21 - B.
11 21 - C.
2 7 - D.
5 7
Discuss
Correct Answer:10 21
Explanation:
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
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