Multiple choice

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. Then $P(X = 1) + P(X = 2)$ equals

  1. $\dfrac {52}{169}$
  2. $\dfrac {25}{169}$
  3. $\dfrac {49}{169}$
  4. $\dfrac {24}{169}$
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B Correct answer
Explanation

Probability of an ace p = 4/52 = 1/13. Probability of no ace q = 12/13. This is a binomial distribution with n=2, p=1/13. P(X=1) = 2 * (1/13) * (12/13) = 24/169. P(X=2) = (1/13)^2 = 1/169. Sum = 25/169.

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