Question

A group of six people play the game of \odd person out" to determine who will buy refreshments. Each person ips a fair coin. If there is a person whose outcome is not the same as that of any other member of the group, this person has to buy the refreshments. What is the probability that there is an odd person out after the coins are ipped once?

Answer 1

The probability is 0.1875

Explanation:

Every person can obtain face or stamp on a coin, so the six people can get 64 ways on this game. This can be calculated with the rule of multiplication as:

2*2*2*2*2*2=64

From this 64 ways we need to find the number of ways in which there is an odd person out. This are the ways in which one person gets different result from others.

There are two ways that apply to this case:

• One person gets face and the others get stamp: this can happen to any of the six people that are playing the game, so there are 6 possibilities in this case.

• One person gets stamps and the others get face: this can happen to any of the six people that are playing the game, so there are 6 possibilities in this case too.

Then, there are 12 ways in which there is an odd person out.

So, the probability can be calculate as:

P=(6+6)/64 = 12/64 = 0.1875