Suppose that your go out for pizza with two freinds You have

Suppose that your go out for pizza with two freinds. You have agreed to the following rule to decide who will pay the bill. Each person will toss a coin. The person who gets a result that is different from the other two will pay the bill. If all three tosses yeild the same result, the bill will be shared by all.

a) list the sample space. (what are the possible combination of the coin toss)

b) find the probability that only you will have to pay

c) find the probability that all three will share the expense.

Solution

Let us define the outcomes of this experiment as follows:

let THH be the outcome that you toss a tail and your two friends toss a head.

Ie. the first letter in this triplet representsyour toss.

The sample space in this instance is S = {TTT, TTH, THT, THH, HTT, HTH, HHT, HHH}.

The event