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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.

Sagot :

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

The number of students play football

[tex]\begin{gathered} =\frac{35}{100}\times100 \\ =35 \end{gathered}[/tex]

The number of students play basket ball

[tex]\begin{gathered} =\frac{22}{100}\times100 \\ =22 \end{gathered}[/tex]

The number of students playing both football and basket ball is

[tex]\begin{gathered} =\frac{15}{100}\times100 \\ =15 \end{gathered}[/tex]

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

[tex]\begin{gathered} P(\text{basketball)}=\frac{7}{100} \\ =0.0070 \end{gathered}[/tex]

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