Multiple choice

From $100$ cards numbered $1$ to $100$, two cardsare drawn one by one with replacement. The probability that both are divisible by $5$ is

  1. $\displaystyle \frac{1}{5}$
  2. $\displaystyle \frac{1}{10}$
  3. $\displaystyle \frac{1}{25}$
  4. $\displaystyle \frac{1}{15}$
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C Correct answer
Explanation

Numbers divisible by 5 between 1 and 100 are 20. Probability of picking one is 20/100 = 1/5. Since replacement occurs, the probability for both is (1/5) * (1/5) = 1/25.

AI explanation

Out of the numbers from 1 to 100, there are exactly 20 numbers divisible by 5. The probability of drawing one such card is 20 divided by 100, which equals 1 divided by 5. Because the draws are made with replacement, the events are independent, so we multiply the individual probabilities: 1 divided by 5 multiplied by 1 divided by 5 equals 1 divided by 25.

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