10 cards are numbered from 1 through 10. The cards are drawn at random. If two cards are drawn with replacement, find the probability of choosing a prime number in both the first and the second draw.
The probability of choosing a prime number in the first draw is 4/10 because there are 4 prime numbers out of 10 (2, 3, 5, and 7).
Since we are drawing with replacement, the probability of choosing a prime number on the second draw is also 4/10.
To find the probability of choosing a prime number in both draws, we need to multiply the probabilities:
(4/10) x (4/10) = 16/100 = 4/25
Therefore, the probability of choosing a prime number in both the first and second draw is 4/25.