Multiple choice

A bag contains $13$ balls numbered from $1$ to $13$. Suppose drawing of an even number is a sucess. Two balls are drawn with replacement from the bag. The probability of getting two successes is

  1. $\dfrac{84}{169}$
  2. $\dfrac{49}{169}$
  3. $\dfrac{36}{169}$
  4. $\dfrac{120}{169}$
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C Correct answer
Explanation

Even numbers in 1 to 13 are 2, 4, 6, 8, 10, 12 (6 numbers). Probability of success = 6/13. Since draws are with replacement, probability of two successes = (6/13) * (6/13) = 36/169.

AI explanation

Since drawing an even number is considered a success and there are 6 even numbers between 1 and 13, the probability of success on a single draw is 6/13. Because the balls are drawn with replacement, we use the binomial probability formula for two successes out of two trials. The probability is (6/13) multiplied by (6/13), which equals 36/169.

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