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Six cards numbered from 1 to 6 are placed in an empty bowl

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Senior Manager
Joined: 16 Apr 2006
Posts: 271
Six cards numbered from 1 to 6 are placed in an empty bowl [#permalink]

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07 Aug 2010, 13:25
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Difficulty:

55% (hard)

Question Stats:

58% (01:04) correct 42% (01:16) wrong based on 55 sessions

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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
[Reveal] Spoiler: OA

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Joined: 02 Sep 2009
Posts: 43378

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07 Aug 2010, 13:30
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Expert's post
There are 6 cards numbered from 1 to 6. They are placed into a box, and then one is drawn and put back and then another card is drawn and put back. What is the probability that one of the cards was 5 if the sum of the two was 8?
(A) 1
(B) $$\frac{2}{3}$$
(C) $$\frac{1}{2}$$
(D) $$\frac{2}{5}$$
(E) $$\frac{1}{3}$$

What combinations of two cards are possible to total 8?
(first card, second card):
(6,2) (2,6) (5,3) (3,5) (4,4) – only 5 possible scenarios for sum to be 8. One from this 5 has already happened. Notice here that the case of (6,2) is different from (2,6), and similarly the case of (5,3) is different from (3,5).

From this five cases, only in two we have 5. So, the probability is 2 chances out of 5 that the one that occurred had 5: P=2/5.

Hope it's clear.
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Re: Six cards numbered from 1 to 6 are placed in an empty bowl [#permalink]

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12 Dec 2017, 23:40
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Re: Six cards numbered from 1 to 6 are placed in an empty bowl   [#permalink] 12 Dec 2017, 23:40
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