Question

This Venn diagram shows sports played by 10 students.PLAYSBASKETBALLMaiPLAYSSOCCERMickeyMarcusFranEllalanKarlJadaGabbyJuanLet event A = The student plays basketball.Let event B = The student plays soccer.What is PAB)?O A.A. «0.17B. 1=0.1010

Answer 1

ANSWER

$P(A|B)=\frac{1}{3}\approx0.333$

EXPLANATION

We want to find the probability P(A|B).

This is a conditional probability and its formula is:

$P(A|B)=\frac{P(A\cap B)}{P(B)}$

where P(A n B) is the probability that the student plays basketball and soccer and P(B) is the probability that the student plays soccer.

We have that:

$P(A\cap B)=\frac{1}{10}$

and

$P(B)=\frac{3}{10}$

Therefore, we have that:

$\begin{gathered} P(A|B)=\frac{1}{10}\div\frac{3}{10} \\ P(A|B)=\frac{1}{10}\cdot\frac{10}{3} \\ P(A|B)=\frac{1}{3}\approx0.333 \end{gathered}$

That is the answer.