Question

A grocer has a bag of fruit containing 3 apples, 2 oranges, and 4 pears. The grocer randomly chooses two pieces of fruit from the bag without looking. What is the probability that the grocer chooses two apples?

Answer 1

Answer:

The probability that the grocer chooses two apples is;

$P=\frac{1}{12}$

Explanation:

Given that;

A grocer has a bag of fruit containing 3 apples, 2 oranges, and 4 pears.

The total number of fruits is;

$\begin{gathered} \text{Apples = 3} \\ \text{Orange = 2} \\ \text{Pears = 4} \\ \text{Total = 3+2+4= 9} \end{gathered}$

Assuming that the grocer did not replace the fruit after picking, the probability of Picking two apples is;

$P=P_1\times P_2$

For the first pick;

$\begin{gathered} P_1=\frac{\text{ number of apple}}{\text{ total number of fruits}}=\frac{3}{9} \\ P_1=\frac{1}{3} \end{gathered}$

For the second pick, the number of apple and the total number of fruits would have reduced by 1;

$\begin{gathered} P_2=\frac{2}{8} \\ P_2=\frac{1}{4} \end{gathered}$

The overall probability is;

$\begin{gathered} P=\frac{1}{3}\times\frac{1}{4} \\ P=\frac{1}{12} \end{gathered}$

Therefore, the probability that the grocer chooses two apples is;

$P=\frac{1}{12}$