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

Given: P(A) = 0.4 , P(B) = 0.8
To find : P(A and B')
Solution: Statement 1 : Since P(A) and P(B) are independent , P(A and B) = P(A) * P(B)
--> We can calculate P(A and B'). Hence sufficient

Statement 2 : Given that P(A)*P(B|A) = 0.32 ----> P(B|A) = 0.32/P(A) = 0.32/0.4 = 0.8
But P(B) = 0.8 Hence P(A) and P(B) are independent. Using same method as in statement 1,
it is sufficient.
Option D.
Hope it helps

Dont forget to give Kudos

Hi Vyshak,
Please change the topic.
Topic and the Q do not match
_________________

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.

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)

Can someone explain how option B is suffice.
_________________

bump...expert please opine on (2). still interested 7 months later :D

bump.. I also don't understand how Info B Suffice.
thx!

Can you please provide the explanation?

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?

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?
Bunuel Please help! I think the question is wrong...

There was a mistake in the condition 2).
It is fixed now.

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.
_________________

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________