Question

Three friends go to a restaurant to have pizza. They decide who will pay for the pizza by tossing a coin. It is decided that each one of them will toss a coin and if one person gets a different result (heads or tails) than the other two, that person would pay. If all three get the same result (all heads or all tails), they will toss again until they get a different result.

1. What is the probability that all three friends will get the same result (all heads or all tails) in one round of tossing?
2. What is the probability that they will get a different result in one round of tossing?
3. What is the probability that they will need exactly four rounds of tossing to determine who would pay?

Answer 1

Let the three friends be A, B and C.

Each toss has 2 outcomes: H or T.

For 3 coins, total outcomes = 2³ = 8

Sample space = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}

a. P(no odd person) = P(HHH) + P(TTT)

= `1/2 xx 1/2 xx 1/2 + 1/2 xx 1/2 xx 1/2`

= `1/8 + 1/8`

= `2/8`

= `1/4`

b. P(odd person) = `1 - 1/4`

= `(4 - 1)/4`

= `3/4`

c. P(odd person in 4^th round) = `1/4 xx 1/4 xx 1/4 xx 3/4`

= `3/256`