# A survey shows that 48% of the respondents like soccer, 66% like basketball, and 38% like hockey. If Meg likes basketball, what is the probability that she also likes soccer?

## 30% like soccer and basketball, 22% like basketball and hockey and 28% like soccer and hockey. 12% like all three.

Mar 27, 2017

$P \left(S | B\right) = 0.455$

#### Explanation:

For brevity:

S = Likes soccer
H=Likes hockey

We are given;

 P(S)=48%=0.48
 P(B)=66%=0.66
 P(H)=38%=0.38
 P(S nn B) = 30% = 0.3
 P(B nn H) = 22% = 0.22
P(S nn H) = 28% = 0.28
 P( S nn B nn H) = 12% = 0.12

And so using the conditional probability formula:

$P \left(S | B\right) = \frac{P \left(S \cap B\right)}{P \left(B\right)}$
$\text{ } = \frac{0.3}{0.66}$
$\text{ } = 0.454545 \ldots$