Question

At the Francis Academy for Boys in Eastern Texas, data from 2019 showed that 35% of all students play football in the fall; 22% of all students play basketball in the winter; and 15% of all students play football and also play basketball. Given that he plays football in the fall, what is the probability that a particular student plays basketball in the winter? Show your work very clearly on your PAPER. Round to 4 decimal place accuracy.

Answer 1

Let's take the total number of students to be 100.

The number of students play football

`\begin{gathered} =(35)/(100)*100 \\ =35 \end{gathered}`

The number of students play basket ball

`\begin{gathered} =(22)/(100)*100 \\ =22 \end{gathered}`

The number of students playing both football and basket ball is

`\begin{gathered} =(15)/(100)*100 \\ =15 \end{gathered}`

By considering the above situation,

From the venn diagram, it is clear that only 7 students play basket ball.

Hence the probability of particular student playing basket ball in winter is

`\begin{gathered} P(\text{basketball)}=(7)/(100) \\ =0.0070 \end{gathered}`