An urn contains three white and four red chips. Each time we draw a chip, we look at its color. If it is red, we replace it along with two new red chips, and if it is white, we replace it along with three new white chips. What is the probability that, in successive drawing of chips, the colors of the rst four chips alternate?

The probability that, in successive drawing of chips, the colors of the first four chips alternate = 0.0751

Step-by-step explanation:

Step 1:

The probability that, in successive drawing of chips, the colors of the first four chips alternate, can occur in two ways: RED-WHITE-RED-WHITE (RWRW) or WHITE-RED-WHITE-RED (WRWR).

Step 2:

Given that an urn contains three white and four red chips and that each time we draw a chip, we look at its color. If it is red, we replace it along with two new red chips, and if it is white, we replace it along with three new white chips.

Probability of RWRW is given as follows:

Probabilty of the first being a red = 4/7

Probability of the next being a white = 3/9 = 1/3

Probability of the next being a red = 6/12 = 1/2

Probability of the next being a white = 6/14 = 3/7

Thus, probability of RWRW = 4/7 × 1/3 × 1/2 × 3/7 = 0.0408

Probability of WRWR is given as follows:

Probabilty of the first being a white = 3/7

Probability of the next being a white = 4/10 =2/5

Probability of the next being a red = 6/12 = 1/2

Probability of the next being a white = 6/15 = 2/5

Thus, probability of WRWR = 3/7 × 2/5 × 1/2 × 2/5 = 0.0343

Step 3:

Probability of RWRW or WRWR = 0.0408 + 0.0343 = 0.0751

Therefore, the probability that, in successive drawing of chips, the colors of the first four chips alternate = 0.0751

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step-by-step explanation: