Q. 2.6 - A First Course in Probability

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?

Step-by-Step Solution

Answer

answer$=0.5$.

Step 1 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.

Step 2 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,

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