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An experiment has 10 equally likely outcomes. Let A and B be two non-e

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shridhar786
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An experiment has 10 equally likely outcomes. Let A and B be two non-e [#permalink] New post   Updated on: 18 Jul 2018, 22:38
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An experiment has 10 equally likely outcomes. Let A and B be two non-empty events of
the experiment. If A consists of 4 outcomes, the number of outcomes that B must have
so that A and B are independent, is


a) 2,4 or 8
b) 3,6 or 9
c) 4 or 8
d) 5 or 10
e) none of these
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D

Originally posted by shridhar786 on 18 Jul 2018, 22:17.
Last edited by chetan2u on 18 Jul 2018, 22:38, edited 1 time in total.
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Re: An experiment has 10 equally likely outcomes. Let A and B be two non-e [#permalink] New post   18 Jul 2018, 22:38
Anything with 10 outcomes because the events are independent.
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Re: An experiment has 10 equally likely outcomes. Let A and B be two non-e [#permalink] New post   18 Jul 2018, 23:16
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shridhar786 wrote:
An experiment has 10 equally likely outcomes. Let A and B be two non-empty events of
the experiment. If A consists of 4 outcomes, the number of outcomes that B must have
so that A and B are independent, is


a) 2,4 or 8
b) 3,6 or 9
c) 4 or 8
d) 5 or 10
e) none of these



Not likely to be tested in GMAT..

But the solution should be...
If two events A and B are independent P(A^B)=P(A).P(B)
here P(A) = 4/10 and let P(B) = x/10
so P(A^B) = \(\frac{4}{10} * \frac{x}{10} = \frac{4x}{100}=\frac{2x}{50}=\frac{2x}{5}/10\)
in (2x/5)/10, 10 are total outcomes and 2x/5 is favorable outcomes...
but favourable outcomes should be an integer so 2x/5 is an integer and x has to be between 0 and 10
so x can be 0, 5 or 10.....
but B is non-empty set, so x cannot be 0..
possible answer 5 and 10

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Re: An experiment has 10 equally likely outcomes. Let A and B be two non-e [#permalink] New post   18 Jul 2018, 23:35
vaibhav1221 wrote:
Anything with 10 outcomes because the events are independent.


total no of outcomes 10 say this S
n(S) = 10 n(A) = 4

for independent event \(\frac{n(A ∩ B)}{n(S)}\) =\(\frac{n(A)}{n(S)}\) * \(\frac{n(B)}{n(S)}\)
- n(S)*n(A ∩ B) = n(A)*n(B)
- 10*n(A ∩ B) = 4*n(B)
- 5*n(A ∩ B) = 2*n(B)
- n(A ∩ B) =\(\frac{2*n(B)}{5}\)
- n(B) can only be 5 or 10 ( n(A ∩ B), n(B) being integers )
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Re: An experiment has 10 equally likely outcomes. Let A and B be two non-e [#permalink] New post   22 Jun 2021, 19:31
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).

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Re: An experiment has 10 equally likely outcomes. Let A and B be two non-e [#permalink]
22 Jun 2021, 19:31
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