Beat The GMAT a GMAT & MBA community

to be accepted at least one school =1- not to be accepted at all


not to be accepted at all =(4/5)*(4/5)*(4/5)=64/125

1-64/125=61/125

_________________
Happy are those who dream dreams and are ready to pay the price to make them come true.(c)

In order to succeed, your desire for success should be greater than your fear of failure.(c)

To be accepted by atleast one school is also equal to OR condition, so why cant it be 1/5 +1/5 + 1/5 = 3/5 ???

Please clarify the confusion???

To be accepted by atleast one school means (1 -to be accepted to NONE school at all)

if ur get OR condition, then u wont get NONE, since Or means that there is some possibibity for being accepted

_________________
Happy are those who dream dreams and are ready to pay the price to make them come true.(c)

In order to succeed, your desire for success should be greater than your fear of failure.(c)

this one is quite easy
step 1: one of 3 schools he will get in :
3!/2!* 20/100*80/100*80/100=48/125
step 2: he will get in 2 in three:
3!/2!*20/100*20/100*80/100=12/125
step 3: he is able to get in all the whole three
3!/3!*20/100*20/100*20/100=1/125
totally =(48+12+1)/125= the answwer

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)
= 61/125

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)
= 61/125

Same Answer. Hooraah!

_________________
Aneesh Bangia
GMAT Math Coach
aneesh.bangia@gmail.com

GMATPad:
Facebook Page: http://www.facebook.com/GMATPad