First slide

Random variable and probability distribution

Question

Two cards are drawn successively with replacement from a well-shuffled deck of 52 cards. Let X denote the random variable of number of aces obtained in the two drawn $cards. If P (X = 1) + P (X = 2) equal k, then \frac{1}{k} =$

Moderate

Solution

$X = number of aces drawn$
$∴ P (X = 1) + P (X = 2)$
$= \{\frac{4}{52} \times \frac{48}{52} + \frac{48}{52} \times \frac{4}{52}\} + \{\frac{4}{52} \times \frac{4}{52}\}$
$= \frac{24}{169} + \frac{1}{169} = \frac{25}{169} = k$
$\Rightarrow \frac{1}{k} = \frac{169}{25} = 6.76$

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