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There are 6 cards numbered from 1 to 6. They are placed into a box, an

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Bunuel
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There are 6 cards numbered from 1 to 6. They are placed into a box, an [#permalink] New post   28 Jan 2022, 04:50
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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 the sum of the two cards will be 8?

A. \(\frac{2}{3}\)

B. \(\frac{1}{2}\)

C. \(\frac{5}{12}\)

D. \(\frac{2}{5}\)

E. \(\frac{5}{36}\)

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Bunuel
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Re: There are 6 cards numbered from 1 to 6. They are placed into a box, an [#permalink] New post   05 Feb 2022, 04:00
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Bunuel wrote:
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 the sum of the two cards will be 8?

A. \(\frac{2}{3}\)

B. \(\frac{1}{2}\)

C. \(\frac{5}{12}\)

D. \(\frac{2}{5}\)

E. \(\frac{5}{36}\)



\(P(sum \ of \ 8) = P(5, 3) + P(3, 5) + P(6, 2) + P(2, 6) + P(4, 4) = \frac{1}{6}*\frac{1}{6} + \frac{1}{6}*\frac{1}{6} + \frac{1}{6}*\frac{1}{6} + \frac{1}{6}*\frac{1}{6} + \frac{1}{6}*\frac{1}{6} = \frac{5}{36}\).


Answer: E.
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Re: There are 6 cards numbered from 1 to 6. They are placed into a box, an [#permalink] New post   28 Jan 2022, 05:04
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Bunuel wrote:
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 the sum of the two cards will be 8?

A. \(\frac{2}{3}\)

B. \(\frac{1}{2}\)

C. \(\frac{5}{12}\)

D. \(\frac{2}{5}\)

E. \(\frac{1}{15}\)



To understand underlying concept better, try the following similar questions:
https://gmatclub.com/forum/there-are-6- ... 80664.html
https://gmatclub.com/forum/there-are-6- ... 55311.html
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Re: There are 6 cards numbered from 1 to 6. They are placed into a box, an [#permalink] New post   28 Jan 2022, 09:17
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Bunuel wrote:
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 the sum of the two cards will be 8?

A. \(\frac{2}{3}\)

B. \(\frac{1}{2}\)

C. \(\frac{5}{12}\)

D. \(\frac{2}{5}\)

E. \(\frac{1}{15}\)



We need to have the sum of the card numbers equal 8
This can be achieved in the following ways:
(2, 6), (3, 5), (4, 4), (5, 3) and (6, 2) => There are 5 different ways

Note: Since its with replacement, we CAN have the case (4, 4) since the card numbered 4 can be picked twice.

Total ways in which 2 cards can be picked (with replacement) = 6 x 6 = 36

Thus, probability = 5/36

Bunuel - Shouldn't the answer be 5/36?
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Re: There are 6 cards numbered from 1 to 6. They are placed into a box, an [#permalink]
28 Jan 2022, 09:17
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