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For a bill to come before the president of the United

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SVP
Joined: 16 Oct 2003
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For a bill to come before the president of the United [#permalink]  04 Nov 2003, 13:29
For a bill to come before the president of the United States, it must be passed by both the House of Representatives and the Senate. Assume that, of the bills presented to these two bodies, 60 percent pass the House, 80 percent pass the Senate, and 90 percent pass at least one of the two. Calculate the probability that the next bill presented to the two groups will come before the president.
Intern
Joined: 04 Oct 2003
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Location: Silicon Valley, CA
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my take on it [#permalink]  04 Nov 2003, 19:40
this is again using
P(A OR B) = P(A) + P(B) - P(A AND B)

Also alteast one of the house gives -->

P(A & ~B) + P(~A & B) + P(A&B)
12/100 + 32/100 + P(A&B) = 9/10

ans 23/50

Is this correct ?
SVP
Joined: 16 Oct 2003
Posts: 1815
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I think the bill is 50% passed. Call for all the prob experts. Answer please
SVP
Joined: 03 Feb 2003
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Two overlapping sets. The total area is 90. The sets are 80 and 60.
90=80+60-X(the overlapping part)
X=50

The overlapping part means that an event (a bill) is in both sets (pass both chambers)
Intern
Joined: 16 Sep 2003
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i do not agree with stolyar....

u are suggesting this

P(A or B)= P(A) + P(B)-P(A AND B) = 9/10

which would give u 50
this is not the case .... because it is clearly states atleast one of the two and not one of the two ....

the exp given by bat_car is correct
SVP
Joined: 03 Feb 2003
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anant wrote:
i do not agree with stolyar....

u are suggesting this

P(A or B)= P(A) + P(B)-P(A AND B) = 9/10

which would give u 50
this is not the case .... because it is clearly states atleast one of the two and not one of the two ....

the exp given by bat_car is correct

I offer overlapping sets.
90 is the total area, which includes A~B, B~A, and AB
at least one of the two means one, the other, or both.
So, I think I am correct
Intern
Joined: 04 Oct 2003
Posts: 42
Location: Silicon Valley, CA
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I agree with stolyar.

My mistake to say that P(A) => PA(~B).
These may or may not mean the same.

So Prob = 50 % is logically correct.

Thanks stolyar.
SVP
Joined: 30 Oct 2003
Posts: 1797
Location: NewJersey USA
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Kudos [?]: 41 [0], given: 0

P(A or B ) = P(A) + P(B) - P(A & B )
so
P( A & B ) = P(A) + P(B) - P(A or B )
= 0.6 + 0.8 - 0.9 = 0.5

----------------------------------------------------------------
But I thought these are independent events.
So
P(A and B ) = 0.6 * 0.8 = 0.48
Can anyone explain why this logic is wrong
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