karthikpandian19 wrote:Can any GMAT Expert explain this one?
Still i m confused????
Ok. Let me try.
Remember: AND implies 'multiplication'. OR implies 'addition'.
Let the names of the three MBA programs be A, B and C.
If for each of A, B, C
P(accepted) = 1/5, then
for each of them
P(not accepted) = 1 - 1/5 =
4/5
Better Method:
P(accepted by atleast one school)
=
1 - P(not accepted by any school)
= 1 - P(not accepted by A) AND P(not accepted by B) AND P(not accepted by C)
= 1 - (4/5)*(4/5)*(4/5)
= 1 - (64/125)
= [spoiler]61/125[/spoiler]
Alternatively(And, this is a long method):
I think you were stuck in the explanation of this method, so I will elaborate it in detail. Read on.
P(accepted by atleast one school)
=
P(accepted by one school) OR P(accepted by two schools) OR P(accepted by three schools)
P(accepted by one school)
= [P(accepted by A) AND P(not accepted by B) AND P(not accepted by C)]*
[Arrange]
Why and What do we arrange?
Notice that we have considered a Yes-No-No for A,B,C but we can also have a No-Yes-No or a No-No-Yes.
The Yes,No,No can be arranged in (3!/2!) = 3 ways.
So,
P(accepted by one school)
= (1/5)*(4/5)*(4/5)*
3
=
48/125
P(accepted by two schools)
= [P(accepted by A) AND P(accepted by B) AND P(not accepted by C)]*
[Arrange]
= (1/5)*(1/5)*(4/5)*3
=
12/125
Note that we have arranged a Yes-Yes-No in 3!/2! = 3 ways here.
P(accepted by 3 schools)
= [P(accepted by A) AND P(accepted by B) AND P(accepted by C)]*
[Arrange]
= (1/5)*(1/5)*(1/5)*
1
=
1/125
Note that there is just one way of arranging Yes-Yes-Yes.
Therefore,
P(accepted by atleast one school)
=
(48/125) +
(12/125) +
(1/125)
= [spoiler]61/125[/spoiler]
Same Answer. Hooraah!
