a basket of fruits contains 5 apples and 3 pears. sharon took two fruits at random. what is the probability…

Explanation:

Step1: Calculate total number of fruits

The total number of fruits is $5 + 3=8$.

Step2: Calculate probability of first - fruit being an apple

The probability that the first fruit is an apple is $\frac{5}{8}$ since there are 5 apples out of 8 total fruits.

Step3: Calculate probability of second - fruit being an apple given first is an apple

After taking one apple, there are 4 apples left and 7 total fruits left. So the probability that the second fruit is an apple given the first is an apple is $\frac{4}{7}$.

Step4: Calculate probability of both being apples

By the multiplication rule of probability for dependent events, the probability that both fruits are apples is $\frac{5}{8}\times\frac{4}{7}=\frac{20}{56}=\frac{5}{14}$.

Answer:

$\frac{5}{14}$