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# M05-34

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Math Expert
Joined: 02 Sep 2009
Posts: 52108

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15 Sep 2014, 23:26
00:00

Difficulty:

5% (low)

Question Stats:

76% (00:38) correct 24% (01:02) wrong based on 135 sessions

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If a fair coin marked 1 and 2, and a fair die are rolled together, what is a probability to have the sum even?

A. $$\frac{1}{8}$$
B. $$\frac{1}{4}$$
C. $$\frac{1}{2}$$
D. $$\frac{3}{4}$$
E. $$\frac{7}{8}$$

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Math Expert
Joined: 02 Sep 2009
Posts: 52108

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15 Sep 2014, 23:26
Official Solution:

If a fair coin marked 1 and 2, and a fair die are rolled together, what is a probability to have the sum even?

A. $$\frac{1}{8}$$
B. $$\frac{1}{4}$$
C. $$\frac{1}{2}$$
D. $$\frac{3}{4}$$
E. $$\frac{7}{8}$$

The coin has 1 and 2, and the die has 1, 2, 3, 4, 5, 6 for a total of 12 possible outcomes.

To get the final result even, we must have two even numbers, $$E$$, or two odd numbers, $$O$$.

$$E + E$$ is possible if we have $$2+2$$, $$2+4$$, $$2+6$$.

$$O + O$$ is possible if we have $$1+1$$, $$1+3$$, $$1+5$$, so there are six favorable outcomes out of 12 possible. $$\frac{6}{12}=\frac{1}{2}$$.

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Intern
Joined: 06 Jul 2014
Posts: 17
WE: Supply Chain Management (Manufacturing)

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24 Nov 2015, 20:32
If a fair coin marked 1 and 2, and a fair die are rolled together, what is a probability to have the sum even?

A. 1/8
B. 1/4
C. 1/2
D. 3/4
E. 7/8

Alt Explanation-
When the fair dice and fair coin numbered 1 and 2 are rolled ,the sum is equally likely to be even or odd.Hence probability is 50%,i.e 1/2.
Intern
Joined: 28 Apr 2016
Posts: 20

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14 Apr 2017, 23:56
1
Hi Bunuel,

For this question I solved like the below. Is it right or just a coincidence?

In order to be sum there are 2 cases:

1) Coin=2 and dice 2,4,6 so together possibility of this 1/2*3/6=1/4
2) Coin=1 and dice 1,3,5 so together 1/2*3/6=1/4

and 1/4+1/4=1/2
Math Expert
Joined: 02 Sep 2009
Posts: 52108

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15 Apr 2017, 01:39
dyg wrote:
Hi Bunuel,

For this question I solved like the below. Is it right or just a coincidence?

In order to be sum there are 2 cases:

1) Coin=2 and dice 2,4,6 so together possibility of this 1/2*3/6=1/4
2) Coin=1 and dice 1,3,5 so together 1/2*3/6=1/4

and 1/4+1/4=1/2

This is absolutely correct approach.
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Re: M05-34 &nbs [#permalink] 15 Apr 2017, 01:39
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# M05-34

Moderators: chetan2u, Bunuel

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