Probability problems
- 1. What is the probability that a non-leap year contains 52 Tuesday only?
Options- A. 1/7
- B. 2/7
- C. 3/7
- D. 6/7 Discuss
Correct Answer: 6/7
Explanation:
A non-leap year has 365 days, each day repeats for 52 times with 1 day left
This one can be {Sun, Mon, Wed, Thu, Fri, and Sat}.
? p = 6/7
- 2. From a pack of 52 playing cards, two cards are drawn together at random. Calculate the probability of both the cards being king?
Options- A. 1/15
- B. 25/57
- C. 35/256
- D. None of these Discuss
Correct Answer: None of these
Explanation:
Two cards can be drawn from a pack of 52 playing cards in 52C2 ways. i,e., 52 x 51 / 2 = 1326 ways. The event that two kings appear in a single drawn of cards is 4C2 ways, i.e 6 ways.
? The probability that the two cards drawn from a pack of 52 cards are kings = 6/1326 = 1/221
- 3. In a bag containing three balls, a white ball was placed and then one ball was taken out at random. What is the probability that the extracted ball would turn on to be white, if all possible hypothesis concerning the colour of the balls that initially in the bag were equally possible?
Options- A. 5/8
- B. 3/4
- C. 1/2
- D. 3/8 Discuss
Correct Answer: 5/8
Explanation:
Since, all possible hypothesis regarding the colour of the balls are equally likely, therefore these could be 3 white balls, initially in the bag.
? Required probability = 1/4 [1 + 3/4 + 1/2 + 1/4]
= 1/4 [(4 + 3 + 2 + 1)/4] = 5/8
- 4. Raja can hit a target 3 times in 6 shots, Karan can hit the target 2 times in 6 shots and Ashwini can hit 4 times in 4 shots. What is the probability that atleast 2 shots hit the target?
Options- A. 1/2
- B. 2/3
- C. 1/3
- D. 5/6 Discuss
Correct Answer: 2/3
Explanation:
Ashwini hits the target definitely, hence required probability that atleast 2 shots hit the target is given by
Karan hits tha target and Raja not hit the target.
or
Karan does not hit the target and Raja hits the target.
or.
Karan hits the target and Raja hits the target
= 2/6 x 3/6 + 4/6 x 3/6 + 2/6 x 3/6
= 24/36 = 2/3
- 5. In his wardrobe, Girdhari has 3 trousers. One of them is grey the second blue and the third brown. In his wardrobe he also has 4 shirts. One of them is grey and the other 3 are white. He opens his wardrobe in the dark and pick out one shirt trouser pair without examination the color. What is the likelihood that neither the shirt nor the trouser is grey?
Options- A. 1/12
- B. 1/6
- C. 1/4
- D. 1/2 Discuss
Correct Answer: 1/2
Explanation:
Probability that trouser is not grey = 2/3
Probability that shirt is not grey = 3/4
? Required probability = 2/3 x 3/4 = 1/2
- 6. A brother and sister appear for an interview against two vacant posts in an office. The probability of the brother's selection is 1/5th and that of the sister's selections is 1/3rd. What is the probability that one of them is selected?
Options- A. 1/5
- B. 2/5
- C. 1/3
- D. 2/3 Discuss
Correct Answer: 1/3
Explanation:
One of them can be selected in the following ways.
Brother is selected and sister is not selected.
or
Brother is not selected and sister is selected.
? Required probability = 1/5 x 2/3 + 4/5 x 1/3
= 2/15 + 4/15 = 6/15 = 2/5
- 7. Two packs of card are thoroughly mixed and shuffled and two cards are drawn at random, one after the other. What is the probability that both of them are jack?
Options- A. 1/13
- B. 2/13
- C. 7/1339
- D. 1/169 Discuss
Correct Answer: 7/1339
Explanation:
Total number of cards = 104
Total number of jacks = 8
? Probability for the jack in first draw = 8/104
and probability for the jack in second draw = 7/103
Since, both are independence events.
? Required probability = 8/104 x 7/103 = 7/1339
- 8. when three coins are tossed together the probability that all coins have the same face up, is?
Options- A. 1/3
- B. 1/6
- C. 1/8
- D. 1/12 Discuss
Correct Answer: 1/8
Explanation:
Probability of head or a tail on upper side of coin = 1/2
? Probability of getting same face on all three coins = 1/2 x 1/2 x 1/2
= 1/8
- 9. Cards are down at random from a pack of 200 cards numbered 1 to 200. Find the probability of drawing a number which is a perfect cube?
Options- A. 1/40
- B. 3/40
- C. 7/40
- D. 19/40 Discuss
Correct Answer: 1/40
Explanation:
Total number of ways of selecting 1 card from 200 cards is 200C1 ways.
Let E be an event of drawing a number which is a perfect cube.
E = {1, 8, 27, 64, 125 }
? P(E) = n(E) / n(S)
= 5C1 / 200C1 = 5/200 = 1/40
- 10. Two unbiased dice are thrown simultaneously. the probability of getting the sum divisible by 3, is?
Options- A. 11/36
- B. 12/36
- C. 13/36
- D. 17/36 Discuss
Correct Answer: 12/36
Explanation:
n(S) = 6 x 6 = 36
n(E) = (1, 2) (2, 1), (1, 5) (2, 4) (3, 3) (4, 2) (5, 1) (3, 6) (4, 5) (5, 4) (6, 3) (6, 6) = 12
? P(E) = 12/36
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