Question

Six fruit baskets contain peaches, apples and oranges. Three of the baskets contain two apples and one orange each, two other baskets contain three apples and one peach each, and the last basket contains two peaches and two oranges. You select a basket at random and then select a fruit at random from the basket. What is the probability that the fruit is an apple?

Answer 1

Dear Student,


$$\begin{gathered} Theprobabilityofchoo\sin ganapple= \\ =\frac{numberofwaysofchoo\sin g3}{totalbaskets}\times \frac{choo\sin g2apples}{total3fruits}+\frac{numberofwaysofchoo\sin g2}{totalbaskets}\times \frac{choo\sin g3apples}{total4fruits}+\frac{numberofwaysofchoo\sin g1}{totalbaskets}\times \frac{choo\sin g0apples}{total3fruits} \\ =\frac{3}{6}\times \frac{2}{3}+\frac{2}{6}\times \frac{3}{4}+\frac{1}{6}\times \frac{0}{3} \\ =\frac{1}{3}+\frac{1}{4} \\ =\frac{7}{12} \end{gathered}$$

Regards,