Probability Question 149
Question: Two cards are drawn successively with replacement from a well shuffled deck of 52 cards then the mean of the number of aces is
[J & K 2005]
Options:
A) 1/13
B) 3/13
C) 2/13
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
Let X denote a random variable which is the number of aces. Clearly, X takes values, 1, 2. $ p=\frac{4}{52}=\frac{1}{13}, $
$ q=1-\frac{1}{13}=\frac{12}{13} $
$ P(X=1)=2\times ( \frac{1}{13} )\times ( \frac{12}{13} )=\frac{24}{169} $
$ P(X=2)=2.{{( \frac{1}{13} )}^{2}}{{( \frac{12}{13} )}^{0}}=\frac{1}{169} $ Mean = $ \sum\limits_{{}}^{{}}{P_{i}X_{i}}=\frac{24}{169}+\frac{2}{169}=\frac{26}{169}=\frac{2}{13} $ .
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