Question

In the Math Club, 7 of the 20 girls are seniors, and 4 of the 14 boys are seniors. What is the probability of randomly selecting a boy or a senior to represent the Math Club at a statewide math contest?

Answer 1

The answer is 21/34.

There are in total 34 children: 20 girls + 14 boys = 34 children
There are in total 11 seniors: 7 senior girls + 4 senior boys = 11 senior children

When we have two events that do not occur together, so only one of the events can happen (there is OR in a sentence), then we use the addition rule and add up probabilities of the events. We have two events not occurring together:
1. The probability of selecting a boy is 14/34 (because there are 14 boys among 34 children).
2. The probability of selecting a senior is 11/34 (because there are 11 seniors among 34 children).


Now, we just need to add them up. However, we have already counted 4 senior boys in the probability of the first event and thus, must subtract the probability of selecting a senior boys (4/34):
14/34 + 11/34 - 4/34 = (14+11-4)/34 = 21/34

Answer 2

34 In All. 14 boys (14/34) 11 Seniors, - 4 so we don't double count. (14/34) + (7/34)