Question

A local university wanted to understand what students prefer to eat during finals. They asked 1,000 students, "Do you prefer chicken, burgers, or pizza?" The results of the survey are shown in the two-way table below:
Chicken Burgers Pizza
Male 127 218 125
Female 219 192 119
What is the probability that a person chosen at random from this survey prefers pizza, given that they are female? Round your answer to the nearest tenth. (2 points)



11.9%
12.5%
22.5%
48.8%

Answer 1

This is an example of conditional probability, which is the probability of an event occurring GIVEN the occurrence of some other event. There is a formula for this $P(A|B)= \frac{P(A and B)}{P(B)}$ 

You want to find the probability that a person chosen at random from this survey prefers pizza, given that they are female. so P(A and B) would refer to the proability that a student is female and prefers pizza. Look at the table and find the intersection of these two events and you would find the probability is $\frac{119}{1000}$. Now find P(B) which is the probability that a student is female. Go to the table, and add up all the boxes where you see a student is female and you would find that P(B) is equal to $\frac{530}{1000}$. Now you wan to plug in these fractions into the formula to find P(A|B) and you get $\frac{119}{1000} /\frac{530}{1000} = \frac{119}{530} = 0.2245.. = 22.5 %$

Answer 2

Given that the person is female, the universe is reduced to 219 + 192 + 119 = 530 people.

The number of women that prefer pizza is 119.

Then the probability is 119/530 *100 = 22.5%