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Probability

Probability - Important Points


21. A box contains 10 red balls and 8 blue balls. Two balls are drawn at random without replacement. What is the probability of getting one red ball and one blue ball?

A. 1/4

B. 20/81

C. 4/27

D. 5/18

Discuss Work Space

Answer: option b

Explanation:

The probability of drawing a red ball on the first draw is 10/18, and the probability of drawing a blue ball on the second draw is 8/17. The probability of drawing a blue ball on the first draw is 8/18, and the probability of drawing a red ball on the second draw is 10/17. To find the combined probability, we add the two cases: (10/18) * (8/17) + (8/18) * (10/17) = 80/306 + 80/306 = 160/306 = 80/153 = 20/81.

22. A bag contains 6 white balls and 4 black balls. Three balls are drawn at random without replacement. What is the probability of getting at least one black ball?

A. 1/7

B. 2/7

C. 3/7

D. 4/7

Discuss Work Space

Answer: option c

Explanation:

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

(4/10) * (3/9) * (2/8) = 24/720, which simplifies to 1/30.

The probability of getting exactly one black ball can be calculated as follows:

(4/10) * (6/9) * (3/8) = 72/720, which simplifies to 1/10.

To find the probability of getting at least one black ball, we subtract the probability of getting no black ball and the probability of getting exactly one black ball from 1: 1 - (1/30 + 1/10) = 1 - (1/30 + 3/30) = 1 - 4/30 = 1 - 2/15 = 13/15.


23. A box contains 5 red balls and 3 blue balls. Three balls are drawn at random with replacement. What is the probability of getting all red balls?

A. 5/243

B. 1/243

C. 125/243

D. 27/243

Discuss Work Space

Answer: option a

Explanation:

The probability of drawing a red ball on each draw is 5/8. Since the balls are drawn with replacement, the probabilities are independent. To find the probability of getting all red balls, we multiply the probabilities: (5/8) * (5/8) * (5/8) = 125/512, which simplifies to 5/243.

24. A fair coin is flipped four times. What is the probability of getting exactly three tails?

A. 1/16

B. 1/8

C. 3/8

D. 1/4

Discuss Work Space

Answer: option c

Explanation:

The probability of getting a tail on each flip is 1/2, and since the flips are independent, we use the binomial probability formula to calculate the probability of getting exactly three tails: (4C3) * (1/2)^3 * (1/2) = 4 * 1/8 * 1/2 = 4/16 = 1/4 = 3/8.

25. A bag contains 7 red candies, 6 green candies, and 5 blue candies. If one candy is randomly chosen, what is the probability of getting a red or green candy?

A. 13/18

B. 1/3

C. 11/18

D. 1/2

Discuss Work Space

Answer: option a

Explanation:

There are 7 red candies and 6 green candies out of a total of 18 candies in the bag. Therefore, the probability of getting a red or green candy is (7 + 6) / 18 = 13 / 18.


Probability Questions and Answers FAQ

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

Probability is an important topic of Quantitative Aptitude. MCQ type Questions with Answers of Probability are required to build your Quantitative Aptitude skills which is a prerequisite for your Career development.

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