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. independent or dependent
The probability of choosing a prime number in both the first and the second draw is independent, as the events do not affect each other due to replacement.
There are 4 prime numbers among the 10 cards (2, 3, 5, 7). The probability of choosing a prime number on the first draw is 4/10, and since the card is replaced, the probability of choosing a prime number on the second draw is also 4/10.
Thus, the probability of choosing a prime number on both draws is (4/10)*(4/10) = 16/100 = 4/25.