Suppose that if a person is randomly chosen in New York, there is a 0,3 probabil

Question

Suppose that if a person is randomly chosen in New York, there is a 0,3 probability that he / she is a
Yankees fan, and a 0,5 probability that he / she is a Jets fan. We are interested the probability that
he / she is either a Yankees fan or a Jets fan under the following different conditions:
(a) What if the probability that he / she is both a Yankees fan and a Jets fan is 0,2?
(b) What if the events he / she is a Yankees fang and he / she is a Jets fang are mutually exclusive?
(c) What if all Yankees fans are Jets fans?
(d) What if all Yankees fans are not Jets fans?
(e) What if the conditional probability of fhe / she is a Jets fan, given that he / she is a Yankees
fan, is one?
(f) What if the conditional probability of he / she is a Yankees fan, given that he / she is a Jets
fan, is 0,2?

Explanation / Answer

P(yankees fan) = 0.3

P(jets fan) = 0.5

P(either yankees fan or jets fan) = P(yankees fan) + P(jets fan) - P(yankees and jets fan)

A) P(yankees and jets fan) = 0.2

P(either yankees and jets fan) = 0.3 + 0.5 - 0.2 = 0.6

B) P(yankees and jets fan) = 0, because they are mutually exclusive.

P(either yankees or jets fan) = 0.3 + 0.5 = 0.8

C) P(yankees and jets fan) = P(yankees fan) = 0.3

P(either yankees or jets fan) = 0.3 + 0.5 - 0.3 = 0.5

D) P(yankees fan and jets fan) = 0

P(either yankees or jets fan) = 0.3 + 0.5 = 0.8

E) P(jets fan | yankees fan) = 1

Or, P(jets fan and yankees fan) / P(yankees fan) = 1

Or, P(jets fan and yankees fan) = 1 * 0.3 = 0.3

P(either yankees or jets fan) = 0.3 + 0.5 - 0.3 = 0.5

F) P(yankees fan | jets fan) = 0.2

Or,P(yankees and jets fan) / P(jets fan) = 0.5

Or, P(yankees fan and jets fan) = 0.5 * 0.2 = 0.1

P(either yankees or jets fan) = 0.3 + 0.5 - 0.1 = 0.7

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