I don\'t understand how to solve this. Please help? Suppose that A, B, and C are
ID: 3150975 • Letter: I
Question
I don't understand how to solve this. Please help?
Suppose that A, B, and C are all independent, mutually exclusive events. Which of the following is the probability of events A or B occurring at the same time that event C occurs?
[ Pr(C) - Pr(A) ] x [ Pr(C) - Pr(B) ]
[ Pr(A) x Pr(B) ] + Pr(C)
1
[Pr(A) x ( 1-Pr(C) )] + [Pr(B) x ( 1-Pr(C) )]
Pr(C) x [ Pr(A) + Pr(B) ]
A)[ Pr(C) - Pr(A) ] x [ Pr(C) - Pr(B) ]
B)[ Pr(A) x Pr(B) ] + Pr(C)
C)1
D)[Pr(A) x ( 1-Pr(C) )] + [Pr(B) x ( 1-Pr(C) )]
E)Pr(C) x [ Pr(A) + Pr(B) ]
Explanation / Answer
Option E is correct.
As, Probability of occuring either of the event A or B at certain time is P(AUB) = P(E) = P(A) +P(B)
where AUB= E
And now at the same time C is occuring and C is idependent of A and B. So Probability of final event is
P(C) * P(E) = P(C) * [ P(A) + P(B)]
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