TS EAMCET · Maths · Probability
Two cards are drawn at random one after the other with replacement from a pack of 52 playing cards. Then the variance of the random variable of the number of spade cards among the drawn cards is
- A \(\frac{3}{8}\)
- B \(\frac{1}{2}\)
- C \(\frac{5}{8}\)
- D \(\frac{7}{8}\)
Answer & Solution
Correct Answer
(A) \(\frac{3}{8}\)
Step-by-step Solution
Detailed explanation
Let \(X\) be the event of getting spade \[ \begin{aligned} & P(X=0)=\frac{39}{52} \times \frac{39}{52}=\frac{9}{16} \\ & P(X=1)=\frac{13}{52} \times \frac{39}{52}=\frac{3}{16} \\ & P(X=2)=\frac{13}{52} \times \frac{13}{52}=\frac{1}{16} \end{aligned} \] \begin{array}{|c|c|c|c|}…
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