basket contains 5 apples and 5 peaches randomly select a piece of fruit and then return it to the basket you randomly select another piece of fruit Find the probability both pieces of fruit are apples

Answer 1

A probability is a number that reflects the chance or likelihood that a particular event will occur.

Here we have two events independent of each other: the first and second fruit picks.

Let us first calculate the probability of picking an apple from the basket in general:

P(A) = total number of apples in the basket / total number of fruits in the basket = 5/10 = 0.5

Now, the probability of first pick to be an apple and the second pick also to be an apple can be written mathematically as,

P(A1) AND P(A2) = P(A1) . P(A2)

Since both picks are independent of each other (as we put the fruit back into the basket after picking the total number of fruits in the basket remains the same each time), P(A1) = P(A2) = P(A) = 0.5

Finally,

P(A1) AND P(A2) = 0.5 x 0.5 = 0.25