Question

Two cards are drawn successively with replacement from a well-shuffled deck of 52 cards. Let Y denote the random variable of number of Jacks obtained in the two drawn cards. Then P(Y = 1) + P(Y = 2) equals?
1. \(\rm \frac{25}{169} \)
2. \(\rm \frac{24}{169} \)
3. \(\rm \frac{5}{169} \)
4. \(\rm \frac{1}{169} \)

Answer 1

Correct Answer - Option 1 : \(\rm \frac{25}{169} \)

Calculation:

P(Y = 1) = P(jack and non jack) + P(non jack and jack)

= \(\rm \frac{4}{52} \times \frac{48}{52} + \frac{48}{52} \times \frac{4}{52} = \frac{24}{169} \)

P(Y = 2) = P(jack and jack) = \(\rm \frac{4}{52} \times \frac{4}{52} = \frac{1}{169} \)

P(Y = 1) + P(Y = 2) = \(\rm \frac{25}{169} \)