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Prob

by artstudent » Sat Aug 13, 2011 1:09 am
The probability that event A occurs is 0.4, and the probability that events A and B both occur is 0.25. If the probability that either event A or event B occurs is 0.6, what is the probability that event B will occur?

Why is the answer not 5/8 and why is the the "either A or B" info relevant?

A and B= A*B => 4/10*(x)=1/4
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by pemdas » Sat Aug 13, 2011 1:33 am
the events A and B are not mutually exclusive.

P(A)=4/10
P(A&B)=25/100
P(A or B)=6/10, find P(B)-?

P(A or B)=P(A)+P(B)-P(A&B), 6/10=4/10+P(B)-25/100, P(B)=9/20
artstudent wrote:The probability that event A occurs is 0.4, and the probability that events A and B both occur is 0.25. If the probability that either event A or event B occurs is 0.6, what is the probability that event B will occur?

Why is the answer not 5/8 and why is the the "either A or B" info relevant?

A and B= A*B => 4/10*(x)=1/4
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by krishnasty » Sat Aug 13, 2011 1:55 am
The formula for conditional probablity is :

P(A U B) = P(A) + P(B) - P(A.B)
Placing the values,
0.6= 0.4 + x - 0.25
Solving, we get,
P(B) = 0.45
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by gmatboost » Mon Aug 15, 2011 9:18 am
artstudent, to directly answer your question:
Why is the answer not 5/8 and why is the the "either A or B" info relevant?
You are assuming that the events are independent, in other words that their probabilities are not related in any way. The question does not tell us that this is the case.
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by GmatKiss » Mon Aug 15, 2011 10:12 pm
P(A)+P(B)-P(A.B)=P(A+B)
0.4+X-0.6=0.25
X=0.25+0.6-0.4
X=0.45

P(B)=0.45
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