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# Q14: Six cards numbered from 1 to 6 are placed in an empty

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Manager
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Q14: Six cards numbered from 1 to 6 are placed in an empty [#permalink]

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08 Jun 2007, 20:50
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Q14:
Six cards numbered from 1 to 6 are placed in an empty bowl. First one card is drawn and then put back into the bowl; then a second card is drawn. If the cards are drawn at random and if the sum of the numbers on the cards is 8, what is the probability that one of the two cards drawn is numbered 5 ?

A. 1/6
B. 1/5
C. 1/3
D. 2/5
E. 2/3
_________________

cool

Manager
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09 Jun 2007, 14:36
ok,let´s try this one...

in order to get an sum 8 from 6 cards numbered 1 to 6 : 1 2 3 4 5 6
with repetition one can have: 2+6 or 3+5 or 4 + 4 or
6+2 or 5+3 or 4+ 4

so the probability that the first card could be a 5 is 1/6
and the probability the second card could be a 5 is 1/6

so 2* 1/6 = 1/3

C????
Director
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09 Jun 2007, 16:14
(D)

This is a conditional probability problem.

P(A|B) = P(A and B) / P(B)

P(A and B) = prob of one of the cards is 5 and sum is 8

5,3 or 3,5 , prob = 2/36 = 1/18

P(B) = prob of sum of 8 = 5/36

now required answer = (1/18)/(5/36) = D
Manager
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10 Jun 2007, 18:34
yes, it appears that we need the prob of getting an 8 ....

3+5
4+4
2+6
5+3
6+2

5/36...

ok I see so 2*1/6*1/6/5/36
Manager
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10 Jun 2007, 18:47
(D)

This is a conditional probability problem.

P(A|B) = P(A and B) / P(B)

P(A and B) = prob of one of the cards is 5 and sum is 8

5,3 or 3,5 , prob = 2/36 = 1/18

P(B) = prob of sum of 8 = 5/36

now required answer = (1/18)/(5/36) = D
Good call. I didn't realize that it had to be conditional and I was stuck there wondering why I kept getting 2/36.
Senior Manager
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13 Jun 2007, 11:00
Getting 8 :
2+6
6+2
3+5
5+3
4+4
total 5 options
there are 2 favorable: 3+5 and 5+3
So the prob witll be 2/5

D
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13 Jun 2007, 12:05
since we already know that the sum of the numbers on the cards is 8 (no need to find out that probability - wording may be misleading !) all we need to do is to figure out what is the probability of geting 5 on one of the draws out of all the "sum 8" draws .

2,6
6,2
5,3
3,5

4,4

hence 2/5 the answer is (D).

13 Jun 2007, 12:05
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