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1-The probability of passing test A is a, The probability of [#permalink]

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07 Dec 2003, 22:39

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A

B

C

D

E

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(N/A)

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1-The probability of passing test A is a, The probability of
passing test B is b, if a student participates in both tests what is
the probability of passing either A or B but not both ?

I didn't know the formula, but I plugged a few numbers and got #2.

I'd like to see someone provide a little theoretical backing. I worry that my "pick some numbers and plug" strategy will backfire in a high stress situation.

Support Racer, P(a or b )=Pa+Pb-P(a and b), Example Pa=50%, Pb=70% P(A or B)=70%+50%-35%=85%, if it was A+B-2AB then it is 120%-70%=50% which makes no sense since the prob of passing either should be higher than the probability of passing a single exam...IMO

Draw a tree diagram , the problem would be easier to see.
Prob of Passing only A = Prob of success in A * Prob of failure in B
= a * (1-b) = a - ab
Similarly, Prob of Passing only B = b * (1-a) = b - ba
The probability of either A or B = a - ab + b - ba = a +b -2ab
its choice (2).

Say there's a 100% chance of passing test a, and a 100% chance of passing test b.

1+1-(1*1) =1

The question asks for "the probability of passing either A or B but not both?". The answer to this question is zero, if the chance of passing each test is 1.