# 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?

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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 #

#### 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 ... #