In a statistic class, there are 18 juniors and 10 seniors, 6 of the seniors are females and 12 of the juniors are males. If a student selected at random, find the probability of having:

Question

a.) a junior or a female

b.) a senior or a female

c.) a junior or a senior

Answer 1

Make a two way frequency table like this:

Then fill in the blanks.

The juniors are the first column. If there are 18 of them and 12 are male then there must be 6 female.

The second column is seniors. If there are 10 total and 6 are female, then 4 must be male.

Now total up the females by adding 6 and 6 to get 12 total females and add the 12 and 4 to get 16 total males. Add either the row total or the column total to get 28 total students.

Now you can calculate probabilities:

1) To find the probability of being a junior or a female, take the total number of juniors (18) then add in the total number of females HOWEVER, you cannot count the 6 that are juniors because you already counted them in the 18. So 18 + 6 (the 6 females that are seniors) = 24. Then take that number out of the total: 24/28 = 6/7

2) To find the probability of being a senior or a female, take the total number of seniors (10) then add in the total number of females HOWEVER, you cannot count the 6 that are seniors because you already counted them in the 10. So 10 + 6 (the 6 females that are juniors) = 16. Then take that number out of the total: 16/28 = 4/7

3) To find the number that is a junior or a senior, you scratch your head and say, aren't they all going to be either a junior or a senior? Probability = 28/28 = 1/1 or 100%