Four friends play a game called Odd Man Out They each flip a

Four friends play a game called Odd Man Out. They each flip a fair coin. If 1 person has heads and the other 3 have tails, then the person with heads is the odd man. Similarly, if 1 person has tails and the other 3 have heads, then the person with tails is the odd man. What is the probability of having an odd man after each person flips just once? Explain your answer.

Solution

Case 1:

1 tails and 3 heads

Choose one friend out of 4 in 4 ways

Then that one friend gets tails and other three ehads in: 1/2^4 ways

So probability is: 4/2^4=1/4

Case 2

3 tails and 1 heads

Choose one friend out of 4 in 4 ways

Then that one friend gets heads and other three tails in: 1/2^4 ways

So probabilty is: 4/2^4=1/4

So   total probability is: 1/4+1/4=1/2