Question

Consider two events, A and B, of a sample space such that P(A) = P(B) =...

Consider two events, A and B, of a sample space such that P(A) = P(B) = 0.7 a).Is it possible that the events A and B are mutually exclusive? Explain. b).If the events A and B are independent, find the probability that the two events occur together. c).If A and B are independent, find the probability that at least one of the two events will occur. d).Suppose P(B|A) = 0.5, in this case are A and B independent or dependent? e).Suppose P(B|A) = 0.9. Find P(A ∪ B)

a)

no as for mutually exclusive event P(A u B) =P(A)+P(B)=0.7+0.7 =1.4

but as probability of an event can not be greater than 1; therefore A and B are not mutually exclusive event

b)

probability that the two events occur together P(A n B)=P(A)*P(B)=0.7*0.7=0.49

c)probability that at least one of the two events will occur.P(A U B)=P(A)+P(B)-P(A n B)

=0.7+0.7-0.49=0.91

d)

here as P(B|A) is not equal to P(B) ;' therefore B depedends on A; hence A and B are dependent

e)

P(A ∪ B) =P(A)+P(B)-P(A)*P(B|A) =0.7+0.7-0.7*0.9=0.77

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