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.
30% like soccer and basketball, 22% like basketball and hockey and 28% like soccer and hockey. 12% like all three.
1 Answer
Mar 27, 2017
P( S | B ) = 0.455 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(S)=48%=0.48
P(B)=66%=0.66 P(B)=66%=0.66
P(H)=38%=0.38 P(H)=38%=0.38
P(S nn B) = 30% = 0.3 P(S∩B)=30%=0.3
P(B nn H) = 22% = 0.22 P(B∩H)=22%=0.22
P(S nn H) = 28% = 0.28 P(S∩H)=28%=0.28
P( S nn B nn H) = 12% = 0.12 P(S∩B∩H)=12%=0.12
And so using the conditional probability formula:
P( S | B ) = (P(S nn B)) / (P(B)) P(S∣B)=P(S∩B)P(B)
" " = 0.3 / 0.66 =0.30.66
" " = 0.454545 ...
