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A basket contains 6 White 4 Black 2 Pink and 3 Green balls. If four balls are picked at random, what is the probability that atleast one is Black?
- a)69/91
- b)80/91
- c)21/91
- d)55/91
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A basket contains 6 White 4 Black 2 Pink and 3 Green balls. If four ba...
Total Balls = 15
Probability = 11c4/15c4 = 22/91
One is black = 1 – 22/91 = 69/91
Probability = 11c4/15c4 = 22/91
One is black = 1 – 22/91 = 69/91
Most Upvoted Answer
A basket contains 6 White 4 Black 2 Pink and 3 Green balls. If four ba...
Solution:
Total number of ways of picking 4 balls out of 15 balls = 15C4
Number of ways of picking 4 balls out of 15 balls such that none is black = 11C4
Number of ways of picking 4 balls out of 15 balls such that atleast one is black = 15C4 - 11C4
= (15 x 14 x 13 x 12) / (4 x 3 x 2 x 1) - (11 x 10 x 9 x 8) / (4 x 3 x 2 x 1)
= 1365 - 330
= 1035
Hence, required probability = 1035 / 15C4
= 69/91
Therefore, the correct answer is option A.
Total number of ways of picking 4 balls out of 15 balls = 15C4
Number of ways of picking 4 balls out of 15 balls such that none is black = 11C4
Number of ways of picking 4 balls out of 15 balls such that atleast one is black = 15C4 - 11C4
= (15 x 14 x 13 x 12) / (4 x 3 x 2 x 1) - (11 x 10 x 9 x 8) / (4 x 3 x 2 x 1)
= 1365 - 330
= 1035
Hence, required probability = 1035 / 15C4
= 69/91
Therefore, the correct answer is option A.
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