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

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Manager
Joined: 16 Apr 2006
Posts: 198
Six cards numbered from 1 to 6 are placed in an empty bowl  [#permalink]

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07 Aug 2010, 14:25
1
2
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Difficulty:

65% (hard)

Question Stats:

50% (01:45) correct 50% (01:53) wrong based on 58 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

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Posts: 56269

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07 Aug 2010, 14:30
1
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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27 Apr 2019, 02:58
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If one of the card is already mentioned that 5 then the other card has to be 3. So
Let assume first the card is 5 is picked and put back. Now probability of getting Card no 3 is 1/5 (we have to exclude 5).
Similarly if the first card drawn is 3 the the probability of getting 5 in the next card is 1/5.

So, In total the probability is 1/5+1/5=2/5
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Manager
Joined: 23 Nov 2016
Posts: 149
Re: Six cards numbered from 1 to 6 are placed in an empty bowl  [#permalink]

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27 Apr 2019, 02:59
If one of the card is already mentioned that 5 then the other card has to be 3. So
Let assume first the card is 5 is picked and put back. Now probability of getting Card no 3 is 1/5 (we have to exclude 5).
Similarly if the first card drawn is 3 the the probability of getting 5 in the next card is 1/5.

So, In total the probability is 1/5+1/5=2/5
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Re: Six cards numbered from 1 to 6 are placed in an empty bowl   [#permalink] 27 Apr 2019, 02:59
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