SOLUTION: Among 140 middle school students, 90 like chocolate ice cream, 70 like strawberry ice cream, and 55 like both. A middle school student is randomly selected. Is liking chocolate

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Question 1172111: Among 140 middle school students, 90 like chocolate ice cream, 70 like strawberry ice cream, and 55 like both. A middle school student is randomly selected.
Is liking chocolate and strawberry ice cream independent events?
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
p(both)=p(c)*p(s) if independent
-
p(c or s)=p(c)+p(s)+p(both),
so putting it in student number
p(c or s)=90+70-55 (55 is double counted)
and 160-55=115 students that like one or the other.
-
so 55/140=(90/140)* (70/140) if independent events
55/140=45/140, which it isn't, so not independent events
Answer by ikleyn(52842)   (Show Source): You can put this solution on YOUR website!
.

In order for to answer the question, we should check if

    P(c)*Ps) = P(c AND s).


From the condition, we have

    P(c) =  = ;  P(s) =  = ;   hence,  P(c)*P(s) =  = .



From the other hand side,

    P(c AND s) =  = .


These calculations show that  P(c)*Ps) =/= P(c AND s);  hence, the events "c" and "s" are NOT INDEPENDENT.

Solved.

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In his post, tutor @Boreal makes many unnecessary calculations, that shade the solution's logic.

So I came with my post to make this logic more clear.



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