Question

A bag 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. $\frac{19}{36}$
• B. $\frac{39}{36}$
  
• C. $\frac{29}{36}$
• D. $\frac{1}{36}$

Answer 1

Answer: (A)

$\frac{19}{36}$

Probability of both apples $=\frac{5}{12}\times \frac{4}{12}=\frac{5}{36}$

Probability of both oranges $=\frac{7}{12}\times \frac{8}{12}=\frac{14}{36}$

Using Total Probability Theorem, we can say

That total probability $=\frac{5}{36}+\frac{14}{36}=\frac{19}{36}$