Answer
The probability that both selections are red is 3/8.
Work Step by Step
An urn contains one red and one white chip and the probability of selecting one chip is 1/2. So the probability of drawing the first red chip is 1/2.
We know that if the first chip drawn is red, we will put back that chip into the urn with two red chips. So, if the first chip drawn is red, we will have 3 red chips and 1 white chip in the urn.
So the probability of drawing second red chip is 3/4.
The probability that both selections are red is calculated as:
\[\begin{align}
& P(\text{both selections are red)}=P(\text{1st draw is red})\times P(2\text{nd draw is red}) \\
& P(\text{both selections are red)}=\frac{1}{2}\times \frac{3}{4} \\
& P(\text{both selections are red)}=\frac{3}{8} \\
\end{align}\]
Therefore, the probability that both selections are red is 3/8.
