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m17, q36

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m17, q36 [#permalink] New post 22 Nov 2009, 04:04
The probability that event A will occur is 20%. If event A occurs, the probability that event B will occur is 30%. What is the probability that event A will occur but event B will not?

1/10
7/55
5/36
7/50
5/24

I agree with OE here, but I do not agree with the solving method.
OE states:
The probability that event A will occur but event B will not = (the probability that event A will occur)*(1 - the probability that event B will occur) =
BUT: the solution is: 1/5*(1-0.3)=1/5*7/10=7/50.

May be I misinterpreted the question stem, but for me the probability that event B WILL occur is 1/5*0.3. Isn't it?
Please, help.
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Re: m17, q36 [#permalink] New post 22 Nov 2009, 05:07
I think the OE is correct. The question asks what is the probability that B will NOT occur.

We want P(A) and P(Not B). This translates to:
P(A) * P(Not B) = P(A) * (1-P(B))
P(A) = 20%
P(B) = 30%
1-P(B) = 1-30% = 70%

P(A) * (1-P(B)) = 20%*70% = 1/5 * 7/10 = 7/50
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Re: m17, q36 [#permalink] New post 29 Oct 2011, 18:41
I disagree with the explanation.

I agree that the final solution is P(A) * [1-P(B)].
& P(A) = 0.2

However regarding P(B) the question says;
" If event A occurs, the probability that event B will occur is 30%"
therefore P(B/A) = 0.3 and not P(B) = 0.3

In the explanation P(B) has been assumed to be 0.3, this does not look right to me.

I think P(B/A) = P (A and B) / P(A) = 0.3 = [P(A) + P(B) - P(A or B)] / P(A)
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Re: m17, q36 [#permalink] New post 24 Feb 2013, 03:49
bunuel,

Why on earth is ' If event A occurs' is included in the question. This doesn't seem alright.

Regards,
SAch
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Re: m17, q36   [#permalink] 24 Feb 2013, 03:49
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