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Question:

Two cards are drawn simultaneously (without replacement) from a well-shuffled pack of 52 cards. Find the mean and variance of the number of red cards.

Mean=0.1and Variance=0.7

Mean=0.6and Variance=0.3

Mean=0.49and Variance=0.37

Mean=0and Variance=0.45

Solution:

Since we have to draw two red cards (without replacement) from 52 cards, therefore the probability is:
p = 26/52 × 25/51 = 25/102
And, q = 1 - 25/102 = 77/102
Since n = 2, therefore,
Mean = np = 2 × 25/102 = 50/102 = 0.49
Variance = npq = 2 × 25/102 × 77/102 = 0.37