Gambling with 4 dice, what is the probability of getting an even sum?

[Gmat_mission]

Gambling with 4 dice, what is the probability of getting an even sum?

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

[spoiler]OA=B[/spoiler]

Source: GMAT Prep

[Scott@TargetTestPrep]

Gambling with 4 dice, what is the probability of getting an even sum?

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

[spoiler]OA=B[/spoiler]

Solution:

Since the sum of the 4 numbers on the dice is either odd or even, we can use the formula:

P(even sum) = 1 - P(odd sum)

To get an odd sum, the 4 numbers on the dice must be 3 odd and 1 even OR 1 odd and 3 even.

P(3 odd and 1 even) = 1/2 x 1/2 x 1/2 x 1/2 x 4C3 = 1/16 x 4 = 1/4

P(1 odd and 3 even) = 1/2 x 1/2 x 1/2 x 1/2 x 4C1 = 1/16 x 4 = 1/4

So, P(odd sum) = 1/4 + 1/4 = 1/2 and therefore, P(even sum) = 1 - 1/2 = 1/2.

Answer: B