Probability problems
- 1. If four balls are picked at random, what is the probability that two are green and two are blue?
Options- A. 1/18
- B. 1/70
- C. 3/5
- D. 1/2 Discuss
Correct Answer: 1/70
Explanation:
Total number of outcomes = 10c4 = 210
Favourable number of outcomes = 3c2 x 2c2 = 3 x 1 = 3
? Required probability = 3/210 = 1/70
- 2. Two cards are drawn at random from a pack of 52 cards. What is the probability that the drawn cards are both aces?
Options- A. 1/221
- B. 2/13
- C. 2/26
- D. None of these Discuss
Correct Answer: 1/221
Explanation:
n(S) = Number of ways of drawing 2 cards out of 52
52C2 = (52 x 51) / (2 x 1) = 1326
n(E) = Number of ways of drawing 2 cards out of 4
= 4C2 = (4 x 3)/2 = 6
? P(E) = 6/1326 = 1/221
- 3. A card is drawn at random 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
- 4. if from each of the three boxes containing 3 white and 1 black, 2 white and 2 black and 1 white and 3 black balls, one ball is drawn at random, then the probability that 2 white and 1 black ball will be drawn is?
Options- A. 13/32
- B. 1/4
- C. 1/32
- D. 3/16 Discuss
Correct Answer: 13/32
Explanation:
You can have
W, W, B or W, B, W or B, W, W
Reqd. probability
= 3/4. 2/4. 3/4 + 3/4. 2/4. 1/4 + 1/4. 2/4. 1/4
= 9/32 + 3/32 + 1/32 = 13/32
- 5. A box contains 3 white and 2 red balls. If we draw one ball and ball and without replacing the first ball. The probability of drawing red ball in the second drawn is?
Options- A. 8/25
- B. 2/5
- C. 3/5
- D. 21/25 Discuss
Correct Answer: 2/5
Explanation:
Total balls in the box = 5
Second red ball can be drawn in two ways
Case I. First ball is white and second ball is red.
Its probability = 3/5.2/4 = 6/20 = 3/10
Case II: First ball is red and second ball is red
Its probability = 2/5.1/4 = 2/20 = 1/10
Hence, reqd. probability
= 3/10 + 1/10 = 4/10 = 2/5
- 6. Three mangoes and three apples are kept in a box. if two fruits are chosen at random. find the probability that one is a mango and the other is an apple.
Options- A. 2/3
- B. 3/5
- C. 1/3
- D. 1/5 Discuss
Correct Answer: 3/5
Explanation:
Total number of ways
= n(s) = 6c2 = 15
Favorable number of ways
= n(E) = 3C1 x 3C1= 9
? Required probability = 9/15 = 3/5
- 7. The probability that a man will be alive for 10 more years is 1/4 and the probability that his wife will alive for 10 more years is 1/3 .The probability that none of them will be alive for 10 more years, is
Options- A. 5/12
- B. 1/2
- C. 7/12
- D. 11/12 Discuss
Correct Answer: 1/2
Explanation:
Required probability = P(A) x P(B)
= (1 - 1/4) x (1 - 1/3) = 3/4 x 2/3 = 1/2
- 8. In a lottery 10000 tickets are sold and ten prizes are awarded. What is the probability of not getting a prize, if you buy one ticket?
Options- A. 9/10000
- B. 9/10
- C. 999/100
- D. 9999/10000 Discuss
Correct Answer: 999/100
Explanation:
Total lottery tickets = 10000
Total prize in the lottery = 10
? Probability getting a prize
= 10/10000 = 1/1000
Now, probability of not getting a prize
= 1 - probability of getting a prize
= 1 - (1/1000)
= 999/1000
- 9. Tow persons A and B appear in an interview for two vacancies. If the probabilities of their selections are 1/3 and 1/6 respectively, then the probability that none of them is selected, is
Options- A. 5/8
- B. 5/12
- C. 1/12
- D. 1/24 Discuss
Correct Answer: 5/8
Explanation:
Required probability = P (A) x p (B)
= (1- 1/4) x (1- 1/6) = (3/4) x (5/6)
= 5/8
- 10. Out of 13 applicants for a job, there are 5 women and 8 men It is desired to select 2 persons for the job, The probability that atleast one of the selected persons will be a woman, is
Options- A. 25/39
- B. 14/35
- C. 5/13
- D. 10/13 Discuss
Correct Answer: 25/39
Explanation:
Total ways = 13c2
Favourable number ways of selecting men only = 8c2
? Probability of selecting no woman
= 8c2 / 13c2
= 14/39
? Probability of selecting at least one woman
= 1 - (14 / 39)
= 25 / 39
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