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
Algebra ->
Probability-and-statistics
-> 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
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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.
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so 55/140=(90/140)* (70/140) if independent events
55/140=45/140, which it isn't, so not independent events
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.
