Answer: B
Cube with 6 sides numbered 1 through 6.
More than 2 times to see sum of all of the rolls are even
P(1)= P(rolling once and not seeing even number) = 3/6 [if 1,3 or 5 happen]
P(2)= P(rolling twice and not seeing even number) = 9/36 = 1/4
first number is 1,3 or 5 and the second number should be in a way which sum of the first and the second is not even: [(1,2), (1,4),(1,6),(3,2), (3,4),(3,6),(5,1),(5,4),(5,6)
P(>2) = 1 - P(1) - P(2) = 1 - 1/2 - 1/4 = 1/4

Let's apply the complement property

P(it takes Jack MORE THAN 2 rolls to get even sum) = 1 - P(it take 2 rolls or fewer to get even sum)

P(it take 2 rolls or fewer to get even sum)
There are exactly two ways in which it can take Jack 2 rolls or fewer to get an even sum:
- Jack rolls an even number on the 1st roll
- Jack rolls an odd number on the 1st roll and then an odd number on the 2nd roll

So, P(it take 2 rolls or fewer to get even sum) = P(even on 1st roll OR odd on first AND odd on 2nd)
= P(even on 1st roll) + P(odd on first AND odd on 2nd)
= 1/2 + (1/2)(1/2)
= 1/2 + 1/4
= 3/4

So, P(it takes Jack MORE THAN 2 rolls to get even sum) = 1 - 3/4
= 1/4

Answer: B

Cheers
Brent

A different way for the probability challenged folk like myself.

In order to have to roll more than twice, we have to look at the even/odd math properties. The question states that Jack stops rolling the dice when the sum is an even number, so what numbers added produce even numbers?

Odd + Odd = Even
Even + Even = Even

Odd + Even = Odd. Aha! This is what we are looking for!

From this property, we know now that the numbers rolled on the dice have to be opposite (If the first one is even, then the second roll has to be odd) and vice versa.

From here, We look at how many numbers can be even or odd on a dice, which is 3 out of 6, or 1/2.

1/2 x 1/2 = 1/4.

The answer is B.

Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.