Question

An urn $A$contains $3$red and$3$black balls, whereas the urn$B$contains $4$red and$6$black balls. If a ball is randomly selected from each urn, what is the probability that the balls will be the same color?

Short answer

answer$=0.5$.

Step-by-step solution

Given Information.

An urn $A$contains $3$red and$3$black balls, whereas the urn $B$contains $4$red and$6$black balls and a ball is randomly selected from each urn.

Explanation.

There are $2$cases:

Case$1:$

Both the balls are red. The probability that the ball chosen from the urn $A$is red is $\frac{3}{6}$and that the ball chosen from the urn $B$is red is$\frac{4}{10}$. These events are independent. Therefore, the total probability is$\frac{3}{6}*\frac{4}{10}$.

Case $2:$

Both the balls are black. The probability that the ball chosen from the urn $A$is black is$\frac{3}{6}$and that the ball chosen from the urn $B$is black is$\frac{6}{10}$. These events are independent. Therefore, the total probability is$\frac{3}{6}*\frac{6}{10}$.

The final probability is the sum of the probabilities in cases $1$and$2$. Therefore,

$\text{answer}=\frac{3}{6}*\frac{4}{10}+\frac{3}{6}*\frac{6}{10}=\frac{30}{60}=0.5$.