Multiple choice

Two cards are drawn successive with replacement from a pack of cards. Taking the random variable X= the variance of X is

  1. $\dfrac{2}{13}$
  2. $\dfrac{9}{13}$
  3. $\dfrac{24}{169}$
  4. $\dfrac{1}{13}$
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C Correct answer
AI explanation

Defining the random variable X as the number of aces drawn, this follows a binomial distribution where n = 2 and p = 4/52 or 1/13. Using the binomial variance formula n*p*(1-p), we substitute the values to get 2 * (1/13) * (12/13). Multiplying these fractions yields 24/169.

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