At a party, the hosts are giving out door prizes. Each guest receives a numbered ticket and a random drawing will be held for the prizes. There are 14 prizes and 22 guests. What is the probability of winning the last prize if multiple winning is not allowed

The probability of winning the last prize is  

Step-by-step explanation:

Total Number of guests = 22

Total Number of prizes = 14

We have to find the probability of winning the last prize. When its turn to announce the last prize, the previous all prizes would have been already distributed. This means, 13 of the prizes would have been already distributed. Since multiple winning is not allowed, the last prize would be distributed in the remaining guests.

After distributing 13 prizes, the number of guests who can win the last prize will be = 22 - 13 = 9

We have only 1 last prize and 9 people among which only 1 will win the prize. Probability is defined as the ratio of favorable outcomes to total number of outcomes.

In this case the favorable outcome is the person with numbered ticket who is going to win a prize. This means favorable outcome is only 1. Total number of outcomes is total number of people remaining, which is 9.

Therefore, the probability of winning the last prize is 1 in 9 i.e.