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Probability

Probability - Important Points


46. A bag contains 10 red cards and 8 black cards. Three cards are drawn at random without replacement. What is the probability of getting exactly two red cards?

A. 3/70

B. 1/56

C. 5/56

D. 5/72

Discuss Work Space

Answer: option b

Explanation:

The probability of getting exactly two red cards can be calculated as follows:

(10/18) * (9/17) * (8/16) = 720/4896, which simplifies to 15/104.

Therefore, the probability of getting exactly two red cards is 15/104 or 1/56.


47. A standard deck of 52 cards is shuffled thoroughly. What is the probability of drawing a black face card (jack, queen, or king)?

A. 1/13

B. 1/26

C. 1/4

D. 3/13

Discuss Work Space

Answer: option c

Explanation:

There are 12 face cards in the deck (jack, queen, and king) out of a total of 52 cards. Out of these 12 face cards, 6 are black (2 black jacks, 2 black queens, and 2 black kings). Therefore, the probability of drawing a black face card is 6/52, which simplifies to 3/26 or 1/4.

48. A bag contains 6 red cards and 4 black cards. Two cards are drawn at random without replacement. What is the probability of getting one red card and one black card?

A. 3/10

B. 2/9

C. 1/4

D. 1/3

Discuss Work Space

Answer: option a

Explanation:

The probability of drawing a red card on the first draw is 6/10, and the probability of drawing a black card on the second draw is 4/9. The probability of drawing a black card on the first draw is 4/10, and the probability of drawing a red card on the second draw is 6/9. To find the combined probability, we add the two cases: (6/10) * (4/9) + (4/10) * (6/9) = 24/90 + 24/90 = 48/90 = 8/15 = 3/5.

49. A standard deck of 52 cards is shuffled thoroughly. What is the probability of drawing a spade card and then a heart card (without replacement)?

A. 1/102

B. 1/51

C. 1/26

D. 1/13

Discuss Work Space

Answer: option b

Explanation:

The probability of drawing a spade card first is 13/52. After one card has been drawn, there are 51 cards left with 13 hearts. The probability of drawing a heart card next is 13/51. To find the combined probability, we multiply the probabilities: (13/52) * (13/51) = 169/2652, which simplifies to 1/51.

50. A bag contains 7 red cards and 5 black cards. Three cards are drawn at random without replacement. What is the probability of getting at least one black card?

A. 23/44

B. 11/44

C. 5/44

D. 7/22

Discuss Work Space

Answer: option d

Explanation:

The probability of getting no black card can be calculated as follows:

(5/12) * (4/11) * (3/10) = 60/1320, which simplifies to 1/22.

To find the probability of getting at least one black card, we subtract the probability of getting no black card from 1: 1 - 1/22 = 21/22. Therefore, the probability of getting at least one black card is 21/22.



Probability Questions and Answers FAQ

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Why do I need to learn Probability Questions with Answers in Quantitative Aptitude?

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