Probability problems
- 1. What is the probability that an ordinary year has 53 Sundays?
Options- A. 53/365
- B. 1/7
- C. 2/7
- D. 48/53 Discuss
Correct Answer: 1/7
Explanation:
An ordinary year has 365 days i,e. 52 weeks and 1 day. So the probability that this day is a Sunday is 1/7.
- 2. One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a face card?
Options- A. 4/13
- B. 1/4
- C. 9/52
- D. 1/13 Discuss
Correct Answer: 4/13
Explanation:
Clearly n(S) = 52 and there are 16 face cards.
? P(E) = 16/52 = 4/13
- 3. One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is either a red card or a king?
Options- A. 6/13
- B. 1/2
- C. 7/13
- D. 27/52 Discuss
Correct Answer: 7/13
Explanation:
Clearly n(S) = 52. There are 26 red cards (including 2 kings ) and there are 2 more kings.
Let (E) be the event of getting either a red card or a king .
Then, n(E) = 28
? P(E) = n(E) / n(S) = 28/52 = 7/13
- 4. What if the probability of getting a king or a queen in a single drawn from a pack of 52 cards?
Options- A. 1/26
- B. 1/13
- C. 2/13
- D. None of these Discuss
Correct Answer: 2/13
Explanation:
Clearly, n (S) = 52, there are 4 kings and 4 queens
? P(E) = n (E) / n (S) = 8/52 = 2/13
- 5. A card is drawn from a pack of 52 cards. A card is drawn at random. What is the probability that it is neither a heart nor a king?
Options- A. 4/13
- B. 9/13
- C. 2/13
- D. 4/13 Discuss
Correct Answer: 9/13
Explanation:
There are 13 hearts and 3 more kings
? p (heart or a king ) = (13 + 3)/52 = 4/13
? P (neither a heart nor a king) = 1 - 4/13 = 9/13
- 6. Seven white balls and three black balls are randomly placed in a row, The probability that no two black balls are placed adjacently equals?
Options- A. 1/2
- B. 7/15
- C. 2/15
- D. 1/3 Discuss
Correct Answer: 7/15
Explanation:
First we place seven white balls at places market W.
W -- W --W --W --W -- W -- W
If we place three black balls at -- places. Then no two black balls will be placed adjacently.
Total No, of -- places = 8
? No. of favourable ways for black balls = 8C3 = 8 x 7 x 6 / 1 x 2 x 3 = 56
Total no. of equally likely cases = 10! / 7!3!
= (10 x 9 x 8) / (1 x 2 x 3) = 15 x 8 = 120
? Reqd. Probability = 56 / 126 = 7/15
- 7. The chance of throwing a total of 3 or 5 or 11 with two dics is?
Options- A. 5/36
- B. 1/9
- C. 2/9
- D. 19/36 Discuss
Correct Answer: 2/9
Explanation:
? Probability for 3 = (1, 2), (2, 1) = 2/36
? Probability for 5 = (1, 4), (2, 3), (3, 2), (4, 1)= 4/ 36
? Probability for 11 (5, 6), (6, 5) = 2/36
? Reqd . Probability = 2/36 + 4/36 + 2/36 = 8/36 = 2/9
- 8. The probability that a man lives after 10 years is 1/4 and that his wife is alive after 10 years is 1/3. The probability that neither of them is alive after 10 years is?
Options- A. 1/2
- B. 1/12
- C. 7/12
- D. 3/4 Discuss
Correct Answer: 1/2
Explanation:
P(M) = 1/4; P(W)= 1/3
? P (M) = 1 - 1/4 = 3/4
? P(W)= 1 - 1/3 = 2/3
Reqd. probability = P(M) P(W) = 3/4 x 2/3 = 1/2
- 9. The probability that a person will hit a target in shooting practice is 0.3 . If he shoots 10 times. Then the probability of his shooting the target is?
Options- A. 1
- B. 1 - (0.7)10
- C. (0.7)10
- D. (0.3)10 Discuss
Correct Answer: (0.3)10
Explanation:
? Probability in each trial (shooting) = 0.3
? Reqd. probability = (0.3)10
- 10. The probability that a marksman will hit a target is given as 1/5. Then his probability of at least one hit in 10 shots, is?
Options- A. 1 - (4/5)10
- B. 1/ (5)10
- C. 1 - 1/ (5)10
- D. (4/5)10 Discuss
Correct Answer: 1 - (4/5)10
Explanation:
? p = 1/5
? q = 1 - 1/5 = 4/5
The probability that none will hit in 10 shots = (4/5)10
? Reqd. probability = 1 - (4/5)10
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