In a survey on ice cream preferences, it was found that 55% of people like vanil

Question

In a survey on ice cream preferences, it was found that 55% of people like vanilla, 55% of people like chocolate, and 50% of people like strawberry. Furthermore, 70% of people like either vanilla or chocolate and 75% of people like either chocolate or strawberry. Also, 35% of people like both vanilla and strawberry and 25% of people like all three flavors. What is the probability that a randomly selected surveyed person likes at most two of these ice cream flavors? What is the probability that a randomly selected surveyed person likes both
vanilla and chocolate?

Explanation / Answer

let probability of liking Vanilla ; Chocolate and Strawberry are A, B and C.

also as P(A n B)=P(A)+P(B)-P(A n B)

a)

probability that a randomly selected surveyed person likes at most two of these ice cream flavors

=1-P(like all of three icecream)=1-0.25 =0.75

b)What is the probability that a randomly selected surveyed person likes both
vanilla and chocolate =P(A n B) =P(A)+P(B)-P(A n C)=0.55+0.55-0.70 =0.40

P(A)= 0.55 P(B)= 0.55 P(C)= 0.5 P(AnB)= 0.4 P(BnC)= 0.3 P(AnC)= 0.35 P(AUB)= 0.7 P(BUC)= 0.75 P(AUC)= 0.7 P(AnBnC) = 0.25

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