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Probability

Probability - Important Points


26. A bag contains 5 red balls and 7 blue balls. Three balls are drawn at random without replacement. What is the probability of getting all blue balls?

A. 35/144

B. 10/144

C. 5/144

D. 1/144

Discuss Work Space

Answer: option a

Explanation:

The probability of getting a blue ball on each draw is 7/12. To find the probability of getting all blue balls, we multiply the probabilities: (7/12) * (6/11) * (5/10) = 35/144.

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

A. 1/9

B. 5/9

C. 9/34

D. 4/9

Discuss Work Space

Answer: option c

Explanation:

The probability of drawing a red ball on the first draw is 10/18, and after one red ball has been drawn, there are 9 red balls left out of 17 balls. The probability of drawing a red ball on the second draw is 9/17. To find the combined probability, we multiply the probabilities: (10/18) * (9/17) = 90/306, which simplifies to 9/34.

28. A bag contains 4 green marbles and 6 blue marbles. Two marbles are drawn randomly with replacement. What is the probability of getting two green marbles?

A. 4/25

B. 9/64

C. 36/100

D. 5/16

Discuss Work Space

Answer: option b

Explanation:

The probability of drawing a green marble on each draw is 4/10. Since the marbles are drawn with replacement, the probabilities are independent. To find the probability of getting two green marbles, we multiply the probabilities: (4/10) * (4/10) = 16/100, which simplifies to 4/25.

29. A bag contains 3 red balls and 5 blue balls. Two balls are drawn at random without replacement. What is the probability of getting one red ball and one blue ball?

A. 6/20

B. 5/16

C. 9/16

D. 1/4

Discuss Work Space

Answer: option b

Explanation:

The probability of drawing a red ball on the first draw is 3/8, and the probability of drawing a blue ball on the second draw is 5/7. The probability of drawing a blue ball on the first draw is 5/8, and the probability of drawing a red ball on the second draw is 3/7. To find the combined probability, we add the two cases: (3/8) * (5/7) + (5/8) * (3/7) = 15/56 + 15/56 = 30/56 = 15/28 = 5/16.

30. A box contains 5 red balls and 7 blue balls. Three balls are drawn at random without replacement. What is the probability of getting exactly one red ball?

A. 10/105

B. 14/105

C. 15/105

D. 20/105

Discuss Work Space

Answer: option b

Explanation:

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

(5/12) * (7/11) * (6/10) = 210/2640, which simplifies to 7/88.

Therefore, the probability of getting exactly one red ball is 7/88.



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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