Multiple choice

From a well shuffled deck of cards, $2$ cards are drawn with replacement. If $x$ represent number of times ace coming, then value of $P(x=1)+P(x=2)$ is

  1. $\dfrac {25}{169}$
  2. $\dfrac {24}{169}$
  3. $\dfrac {49}{169}$
  4. $\dfrac {23}{169}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

With replacement, the probability of an ace on each draw is 1/13. Thus P(x = 1) = 2(1/13)(12/13) = 24/169 and P(x = 2) = 1/169, giving 25/169.

AI explanation

The number of aces follows a binomial distribution with 2 trials and a probability of drawing an ace of 1 divided by 13. Using the binomial probability formula, P(x=1) is calculated as 2 multiplied by (1 divided by 13) multiplied by (12 divided by 13), which equals 24 divided by 169. P(x=2) is (1 divided by 13) squared, which equals 1 divided by 169, so the sum of the two probabilities is 25 divided by 169.

Keep practicing — related questions