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coin + dice

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by AIM GMAT » Wed Mar 23, 2011 8:19 am
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

[spoiler]OA : 1/2[/spoiler]
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by manpsingh87 » Wed Mar 23, 2011 8:28 am
AIM GMAT wrote: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

[spoiler]OA : 1/2[/spoiler]
sum would be even in two case 1)Odd(coin) and odd(dice)
2) even(coin) and even(dice)

probablity of odd getting in case of coin is 1/2;and in dice it is 3/6 i.e. 1/2

therefore required probability is (1/2)(3/6)+(1/2)(3/6)=1/2 hence c
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by force5 » Wed Mar 23, 2011 9:03 am
IMO- 1/2

total cases 12 ( 6+6)
if coin is 1 then possible cases with dice - 1,3,5
if coin is 2 then - 2, 4, 6

prob to get even = 6/12 = 1/2

hope it helps....
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by GMATGuruNY » Wed Mar 23, 2011 10:49 am
AIM GMAT wrote: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

[spoiler]OA : 1/2[/spoiler]
The coin and the die are indistinguishable from each other:
1/2 the outcomes on the coin are odd, the other half even.
1/2 the outcomes on the die are odd, the other half even.

Thus, the question can be rephrased:
If the coin is flipped twice, what is the probability that the sum will be even?

4 potential outcomes:
1 + 1 = 2.
1 + 2 = 3.
2 + 1 = 3.
2 + 2 = 4.

Since 2 of the 4 possible sums are even, P(even sum) = 1/2.

The correct answer is C.
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