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

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The probability that event A occurs is 0.4 and the probability that  [#permalink]

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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.
Spoiler: OA

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Originally posted by MathRevolution on 14 May 2016, 02:56.
Last edited by MathRevolution on 16 Sep 2017, 07:32, edited 2 times in total.
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Re: The probability that event A occurs is 0.4 and the probability that  [#permalink]

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New post 14 May 2016, 10:23
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Hi Vyshak,
Please change the topic.
Topic and the Q do not match
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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

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New post 16 May 2016, 20:01
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]

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New post 05 Jun 2016, 22:33
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]

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New post 09 Jul 2016, 07:34
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]

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New post 14 Feb 2017, 22:44
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]

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New post 14 Sep 2017, 04:34
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]

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New post 14 Sep 2017, 11:43
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]

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New post 14 Sep 2017, 18:57
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]

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New post 14 Sep 2017, 21:26
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...
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Re: The probability that event A occurs is 0.4 and the probability that  [#permalink]

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New post 16 Sep 2017, 07:36
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]

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New post 16 Sep 2017, 10:49
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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 :)

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Re: The probability that event A occurs is 0.4 and the probability that &nbs [#permalink] 16 Sep 2017, 10:49
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