Question Video: Finding a Conditional Probability Using a Two-Way Table Mathematics • Third Year of Secondary School

Join Nagwa Classes

Attend live Mathematics sessions on Nagwa Classes to learn more about this topic from an expert teacher!

The table contains data from a survey of students who were asked whether their preferred sport was baseball, soccer, or hockey. The results are split by gender. Given that a student prefers baseball, find the probability that they are female. Give your answer to three decimal places.

01:04

Video Transcript

The table below contains data from a survey of students who were asked whether their preferred sport was baseball, soccer, or hockey. The results are split by gender. Given that a student prefers baseball, find the probability that they are female. Give your answer to three decimal places.

Let’s denote baseball by 𝐵 and female by 𝐹. The probability of 𝐹 given 𝐵 is the number of female baseball preferers divided by the total number of baseball preferers. To find the total baseball, we simply sum all of the entries in the baseball row of the table. This sum is 118.

We can now substitute in our value of 72 female baseball preferers from the table and the total of 118 that we have just calculated. 72 divided by 118 equals 0.610 to three decimal places, which is the probability that we were asked to find.