Question

An urn contains one red chip and one white chip. one chip is drawn at random. if the chip selected is red, that chip together with two additional red chips are put back into the urn. if a white chip is drawn, the chip is returned to the urn. then a second chip is drawn. what is the probability that both selections are red?

Answer 1

Solution: We are given an urn contains 1 red chip and 1 white chip.

Now let's consider the first draw.

The probability of drawing red chip $=\frac{1}{2}$

We know that if the first chip drawn is red, we will put back that chip into the urn with additional two red chips. So if the first chip drawn is red, we will have 3 red chips and 1 white chip in the urn.

Now if we draw another chip from an urn containing 3 red chips and 1 white chip. Then the probability of drawing a red chip is

$= \frac{3}{4}$

Now lets combine these two events

The probability of both are red = P(1st draw is red) . P(2nd draw is red)

                                                   =(1/2) x (3/4)

                                                   =(3/8)

Therefore, the probability of both selections are red is 3/8