Question

A basket contains $5$ apples and $7$ oranges and another basket contains $4$ apples and $8$ oranges. One fruit is picked out from each basket. Find the probability that the fruits are both apples or both oranges

• A. $\frac{24}{144}$
• B. $\frac{56}{144}$
• C. $\frac{68}{144}$
• D. $\frac{76}{144}$

Answer 1

The correct option is D

$\frac{76}{144}$

Explanation for the correct option:

Finding the probability that the fruits are both apples or both oranges:

A basket contains $5$ apples and $7$ oranges

Second basket contains $4$ apples and $8$ oranges

The probability that both fruits are apples $=\frac{5}{12}\times \frac{4}{12}$

$=\frac{20}{144}$

The probability that both fruits are oranges $=\frac{7}{12}\times \frac{8}{12}$

$=\frac{56}{144}$

$\therefore$The probability that fruits are both apples or both oranges $=\frac{20}{144}+\frac{56}{144}$

$$\begin{gathered} =\frac{20+56}{144} \\ =\frac{76}{144} \end{gathered}$$

Hence, option ‘D’ is correct.