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There are three boxes each containing 3 Pink and 5 Yellow balls and also there are 2 boxes each containing 4 Pink and 2 Yellow balls. A Yellow ball is selected at random. Find the probability that Yellow ball is from a box of the first group?
- a)42/61
- b)45/61
- c)51/61
- d)52/61
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
There are three boxes each containing 3 Pink and 5 Yellow balls and al...
Probability = (3/5 * 5/8)/([3/5 * 5/8] + [2/5 * 1/3]) = 45/61
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Most Upvoted Answer
There are three boxes each containing 3 Pink and 5 Yellow balls and al...
Solution:
Total number of Yellow balls: 3*5 + 3*5 + 2*2 = 25
Number of Yellow balls in the first three boxes: 3*5 + 3*5 = 30
Number of Yellow balls in the last two boxes: 2*2 = 4
Let E be the event of selecting a Yellow ball from the first group of boxes.
P(E) = (number of Yellow balls in the first group) / (total number of Yellow balls)
P(E) = 30 / 25 = 6 / 5
The probability that a Yellow ball is from a box of the first group is 6/5 which is not possible. Therefore, the correct probability is the complement of this event.
P(Yellow ball is not from the first group) = 1 - P(E)
P(Yellow ball is not from the first group) = 1 - 6/5
P(Yellow ball is not from the first group) = 1/5
Therefore, the probability that the Yellow ball is from a box of the first group is:
P(E) = 1 - P(Yellow ball is not from the first group)
P(E) = 1 - 1/5
P(E) = 4/5
Hence, the correct option is (B) 45/61.
Total number of Yellow balls: 3*5 + 3*5 + 2*2 = 25
Number of Yellow balls in the first three boxes: 3*5 + 3*5 = 30
Number of Yellow balls in the last two boxes: 2*2 = 4
Let E be the event of selecting a Yellow ball from the first group of boxes.
P(E) = (number of Yellow balls in the first group) / (total number of Yellow balls)
P(E) = 30 / 25 = 6 / 5
The probability that a Yellow ball is from a box of the first group is 6/5 which is not possible. Therefore, the correct probability is the complement of this event.
P(Yellow ball is not from the first group) = 1 - P(E)
P(Yellow ball is not from the first group) = 1 - 6/5
P(Yellow ball is not from the first group) = 1/5
Therefore, the probability that the Yellow ball is from a box of the first group is:
P(E) = 1 - P(Yellow ball is not from the first group)
P(E) = 1 - 1/5
P(E) = 4/5
Hence, the correct option is (B) 45/61.
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