a bag of fruit contains 4 apples, 1 plum, 2 apricots, 3 oranges. Pieces of fruit are drawn twice with replacement. What is p(apple, then apricot)?

4/5, 2/25, 3/25, 3/5
I chose 3/5

If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.

4/10 * 2/10 = 3/25

ok i see thanks

4/10 * 2/10 = 2/5 * 1/5 ≠ 3/25

To find the probability of drawing an apple and then an apricot, we need to calculate two separate probabilities: the probability of drawing an apple and the probability of drawing an apricot given that an apple has already been drawn.

Let's calculate each probability separately:

Probability of drawing an apple:
In the bag of fruit, there are a total of 10 pieces of fruit (4 apples + 1 plum + 2 apricots + 3 oranges). So, the probability of drawing an apple on the first draw is 4/10.

Probability of drawing an apricot given that an apple has already been drawn:
After the first draw, regardless of whether an apple or any other fruit was drawn, the piece of fruit is returned to the bag, and the bag is shuffled. So, the probability of drawing an apricot on the second draw is still 2/10 since the number of apricots remains the same.

Now, we multiply the probabilities of both events (drawing an apple and then drawing an apricot) to find the overall probability:

P(apple, then apricot) = P(apple) × P(apricot|apple)
P(apple, then apricot) = (4/10) × (2/10)
P(apple, then apricot) = 8/100
P(apple, then apricot) = 2/25

So, the correct answer is 2/25, not 3/5.