Out of a group of 100 people, 23 are at least 180 cm tall, 35 arc fans of The Bi

Question

Out of a group of 100 people, 23 are at least 180 cm tall, 35 arc fans of The Big Bang Theory and 33 eat chocolate cake for breakfast. Furthermore, 15 are at least 180 cm tall and are fans of The Big Bang Theory, 19 are at least 180 cm tall and eat chocolate cake for breakfast, 18 are fans of the Big Bang Theory and cat chocolate cake for breakfast, and 12 are at least 180 cm tall, are fans of the Big Bang Theory and eat chocolate cake for breakfast. (When we say. for instance, that 18 are fans of the Big Bang Theory and cat chocolate cake for breakfast, we include, as usual, the 12 who have all three properties.) Find the probability that a randomly selected member of the group is not a fan of The Big Bang Theory and is not at least 180 cm tall. Find the probability that a randomly selected member of the group is at least 180 cm tall, but is not a fan of The Big Bang Theory. Given that a randomly selected member of the group is not at least 180 cm tall, find the probability that he does not cat chocolate cake for breakfast.

Explanation / Answer

A)

P( not a fan of big ban theory and is not at least 180 cm tall) = 1 - 15/100 = 0.85

B)

P( at least 180 tall but not a fan of big bang theory) = 23/100 - 15/100 = 0.08

C)

P(not eat chocolate / is not at least 180 tall) = [ 19/100 / 23/100] = 0.826

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