Problem 19STE

When three friends go for coffee, they decide who will pay the check by each flipping a coin and then letting the “odd person” pay. If all three flips produce the same result (so that there is no odd person), then they make a second round of flips, and they continue to do so until there is an odd person. What is the probability that

(a) exactly 3 rounds of flips are made?

(b) more than 4 rounds are needed?

Solution :

Step 1 of 2:

Given when 3 coins are flipped, there are 8 cases or in 3 flips of coin possible outcomes are .

Then the probability when no odd person is there =

So the probability when no odd person is there =

Our goal is:

a). We need to find the probability of exactly 3 rounds of flips are made.

b). We need to find the probability of more than 4 rounds are needed.

a). The probability of exactly 3 rounds of flips are made is

P( exactly 3 rounds of flips) =

P( exactly 3 rounds of flips) =

P( exactly 3 rounds of flips) =

P( exactly 3 rounds of flips) = 0.04685

Therefore, the probability of exactly 3 rounds of flips are made is 0.04685.