Answer:
The probability is;
[tex]P(\text{Junior}\cap\text{Soccer)}=0.15[/tex]
Explanation:
From the given table;
The percentage of students that are juniors is;
[tex]33\text{\%}[/tex]
The percentage of the juniors that chose soccer a their favorite sport is;
[tex]45\text{\%}[/tex]
So, The probability rounded to the nearest hundredth that any student selected from all three grades is a junior who listed soccer as their favorite sport is;
[tex]P(\text{Junior}\cap\text{Soccer)}=P(\text{Junior)}\times P(Soccer)[/tex]
Substituting the percentages we have;
[tex]\begin{gathered} P(\text{Junior}\cap\text{Soccer)}=33\text{\%}\times45\text{\%}=\frac{33}{100}\times\frac{45}{100} \\ P(\text{Junior}\cap\text{Soccer)}=\frac{1485}{10000} \\ P(\text{Junior}\cap\text{Soccer)}=0.1485 \\ P(\text{Junior}\cap\text{Soccer)}=0.15 \end{gathered}[/tex]
Therefore, the probability is;
[tex]P(\text{Junior}\cap\text{Soccer)}=0.15[/tex]
