Question

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.

Answer 1

`P( S | B ) = 0.455`

Explanation:

For brevity:

S = Likes soccer
B=Likes basketball
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( S | B ) = (P(S nn B)) / (P(B))`
`" " = 0.3 / 0.66`
`" " = 0.454545 ...`