Probability problems
- 1. 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 |
- 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?
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 |
- 3. 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 |
- 4. 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 ` | ||||
|
||||
| = 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 | ||||
|
||||
| = 10. |
| ∴ P(E) = | n(E) | = | 10 | . |
| n(S) | 21 |
- 5. In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?
Options- A.
1 10 - B.
2 5 - C.
2 7 - D.
5 7
Discuss
Correct Answer:
| 2 |
| 7 |
Explanation:
| P (getting a prize) = | 10 | = | 10 | = | 2 | . |
| (10 + 25) | 35 | 7 |
- 6. What is the probability that a number selected from the numbers 1, 2, 3, 4, 5....16 is a prime number?
Options- A. 1/16
- B. 5/8
- C. 3/8
- D. 7/16 Discuss
Correct Answer: 3/8
Explanation:
S = {1, 2, 3, ......16}
E = {2, 3, 5, 7, 11, 13}
? P(E) = n(E)/n(S) = 6/16= 3/8
- 7. An urn contains 9 red, 7 white and 4 black balls. A ball is drawn at random. What is the probability that the ball drawn is not red?
Options- A. 1/11
- B. 9/20
- C. 2/11
- D. 11/20 Discuss
Correct Answer: 11/20
Explanation:
P (red) = 9 / (9 + 7 + 4) = 9/20
? P(not-red) = (1 - 9/20) = 11/20
- 8. In a lottery there are 20 prizes and 15 blanks. What is the probability of getting prize?
Options- A. 1/10
- B. 2/5
- C. 4/7
- D. 2/7 Discuss
Correct Answer: 4/7
Explanation:
P (getting a prize ) = 20 / (20 + 15 ) = 20 / 35 = 4/7
- 9. The odds in favour of an event are 3 : 5. The probability of occurrence of the event is?
Options- A. 3/5
- B. 3/8
- C. 1/3
- D. 1/5 Discuss
Correct Answer: 3/8
Explanation:
Number of cases favourable of E = 3
Total Number of cases = (3 + 5 ) = 8
? P(E) = 3/8
- 10. The probability of getting heads in both trials when a balanced coin is tossed twice will be?
Options- A. 1/4
- B. 1/2
- C. 1
- D. 3/4 Discuss
Correct Answer: 1/4
Explanation:
Probability of getting head in one trail = 1/2
? Reqd Probability of getting heads in both the trails = 1/2 x 1/2 = 1/4
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