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Probability of A or B

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by GmatKiss » Sat Oct 15, 2011 2:14 pm
The events A and B are independent. The probability that event A occurs is 0.6, and the probability that at least one of the events A or B occurs is 0.94. What is the probability that event B occurs?

(A) 0.34

(B) 0.65

(C) 0.72

(D) 0.76

(E) 0.85

Looking for a formula to deal with this one!
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by n@resh » Sat Oct 15, 2011 4:32 pm
GmatKiss wrote:The events A and B are independent. The probability that event A occurs is 0.6, and the probability that at least one of the events A or B occurs is 0.94. What is the probability that event B occurs?

(A) 0.34

(B) 0.65

(C) 0.72

(D) 0.76

(E) 0.85

Looking for a formula to deal with this one!
Atleast one event = 1 - ( not P(A) AND not P(B)) = 0.94
=> 1 - ( (1 - 0.6) * ( 1 - B) ) = 0.94
1 - 0.4(1-B) = 0.94
0.4(1 - B) = 0.06
1 - B = 6/40 => B = 34/40 = 0.85
Hence E!
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by HeyArnold » Sun Oct 16, 2011 6:42 am
n@resh--thanks for your answer.


Can anyone help me understand why this isn't as simple as:

P(A) or (B) = P(A) + P(B)

So 0.6 + P(B) = 0.94
P(B) = 0.88

?

thanks!
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