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If the probability that Mike can win a championship is 1/4, [#permalink]
26 Jul 2007, 23:38

If the probability that Mike can win a championship is 1/4, and that of Rob winning is 1/3 and that of Ben winning is 1/6, what is the probability that Mike or Rob win the Championship but not Ben ?

Re: Conceptual Probability Question [#permalink]
27 Jul 2007, 12:04

ajay_gmat wrote:

If the probability that Mike can win a championship is 1/4, and that of Rob winning is 1/3 and that of Ben winning is 1/6, what is the probability that Mike or Rob win the Championship but not Ben ?

1) 1/6 2) 5/12 3) 7/12 4) 5/6 5) 1

imo, it is

(prob that mike or rob win) (prob that ben won't win) = (1/4 + 1/3) (1 - 1/6) = 35/72

But am going wrong somewhere obviously.. Could you help me out..

they are all exclusive events
(i.e. both people can't win) therefore they are not independant events

Pr A or B = Pr( A) + Pr (B) - Pr( A ANDB)

1/4+1/3=7/12

it might be conceptually simpler to construct two complementary events that sum to 1, PR Ben will win + PR Ben won't win - but that doesn't work in this situation because like others stated we are missing another person.

why are we subtracting Ben's probability of winning?

P(AorB) = P(A) + P(B) - (PAandB)

there can be only one winner so P(AandB)=0

saying P A or B but not C has no meaning because if A or B wins, C can't win.

we are missing another contestant, 'D', with a 3/12 chance of winning... C+D = 5/12.

just seems weird to me.

Yeah I don't really get it... but that's the math rule or something

i hate rules that i don't understand. i will get any problem of this ilk wrong on the gmat, because i don't understand the logic behind it.

this is GMAT prep at its worst. employing a rule/concept you don't understand because you are told it is right.

Just think about it this way:
The total probability at least ONE of them wins:
P(Mike Wins) + P(Rob Wins) + P(Ben Wins) = 9/12

If they told you that you could not count on Ben winning, so now what are the chances of total win between Mike and Rob with Ben's loss?
-- Here you're subtracting the possibility of Ben winning all together from their combined probability. So:
P(Mike) + P(Rob) - P(Ben) = 7/12