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# The probability that event A occurs is 0.4 and the probability that

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Math Revolution GMAT Instructor
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Re: The probability that event A occurs is 0.4 and the probability that [#permalink]
You only have to find out P(A∩B) in the original condition. Hence, there is only 1 variable, which means D is likely the answer. Using the condition 1) and the condition 2), we can see that the condition 1) is essentially the same as the condition 2) (1)=2)). So, the correct answer is D.

- Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
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Re: The probability that event A occurs is 0.4 and the probability that [#permalink]
MathRevolution wrote:
The probability that event A occurs is 0.4 and the probability that event B occurs is 0.8. What is the probability that event A occurs but not event B?

1) Event A and event B are independent.
2) The probability that neither event A nor event B occurs is 0.32.

* The answer will be posted in two days.

for (2) do you mean the probability both happen? Correct me if I'm wrong:

Prob(both): .4 * .8 = .32 (if both indep)
Prob(neither): .6 * .2 = .12 (if both indep)
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Re: The probability that event A occurs is 0.4 and the probability that [#permalink]
MathRevolution wrote:
The probability that event A occurs is 0.4 and the probability that event B occurs is 0.8. What is the probability that event A occurs but not event B?

1) Event A and event B are independent.
2) The probability that neither event A nor event B occurs is 0.32.

* The answer will be posted in two days.

Can someone explain how option B is suffice.
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Re: The probability that event A occurs is 0.4 and the probability that [#permalink]
bump...expert please opine on (2). still interested 7 months later :D
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Re: The probability that event A occurs is 0.4 and the probability that [#permalink]
bump.. I also don't understand how Info B Suffice.
thx!
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Re: The probability that event A occurs is 0.4 and the probability that [#permalink]
MathRevolution wrote:
You only have to find out P(A∩B) in the original condition. Hence, there is only 1 variable, which means D is likely the answer. Using the condition 1) and the condition 2), we can see that the condition 1) is essentially the same as the condition 2) (1)=2)). So, the correct answer is D.

- Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Can you please provide the explanation?
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Re: The probability that event A occurs is 0.4 and the probability that [#permalink]
Statement tells probability of neither a nor b. So,would'nt it be like this:(1-P(A)) * (1-P(B)), which comes out to be 0.12 ?
Can anyone please point out where I am going wrong in this?
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Re: The probability that event A occurs is 0.4 and the probability that [#permalink]
Since statement (2) does not state A and B are independent events, I have assumed the following:

a - Represents probability that only event A occurs
b - Represents probability that only event B occurs
c - Represents probability that both events A&B occur
d - Represents probability that neither A nor B occurs

Therefore, a+b+c+d = 1
a+c=0.4, b+c=0.8 and according to statement (2) d=0.32
We want to find the probability that only A occurs and B does not occur i.e "a"
a+b+2c = 1.2
a+b+c = 1-d = 0.68
c=0.52

Now a+c = 0.4 Therefore a= -0.12 But, how can a probability be NEGATIVE?
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Re: The probability that event A occurs is 0.4 and the probability that [#permalink]
MathRevolution wrote:
The probability that event A occurs is 0.4 and the probability that event B occurs is 0.8. What is the probability that event A occurs but not event B?

1) Event A and event B are independent.
2) The probability that event A and event B occur together is 0.32.

* The answer will be posted in two days.

There was a mistake in the condition 2).
It is fixed now.
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Re: The probability that event A occurs is 0.4 and the probability that [#permalink]
I like this question a lot and it's a reminder for me to guard against what I can only assume is another common GMAT trap. Always mentally check whether the events are independent. That makes a difference.

The probability that event A occurs is 0.4 and the probability that event B occurs is 0.8. What is the probability that event A occurs but not event B?

From the stem, we know that ...

P(A) = 0.4
P(B) = 0.8
P(A and B) = 0.32 <--- Wait! We don't actually know if A and B are independent. If they aren't, then this won't hold true.

The question is:
P(A and ~B) = P(A) x P(~B) = ?

1) Event A and event B are independent.
P(A and ~B) = P(A) x P(~B) = 0.4 x (1-0.8) = 2/25

Sufficient.

2) The probability that event A and event B occur together is 0.32.
P(A and B) = 0.32 = P(A) x P(B) <--- It MUST be true then that A and B are independent.

So...P(A and ~B) = P(A) x P(~B) = 0.4 x (1-0.8) = 2/25

Sufficient.

D.
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Re: The probability that event A occurs is 0.4 and the probability that [#permalink]
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Re: The probability that event A occurs is 0.4 and the probability that [#permalink]
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