5lb book, chap-23, no- 40

[anik1989]

Jack has a cube with 6 sides numbered 1 through 6. He rolls the cube repeatedly until the first time that the sum of
all of his rolls is even, at which time he stops. (Note: it is possible to roll the cube just once.) What is the
probability that Jack will need to roll the cube more than 2 times in order to get an even sum?

[tommywallach]

Hey Anik,

This question requires using the 1-x trick.

The odds that Jack will stop on the first roll + the odds that Jack will stop on the second roll + the odds that Jack will stop AFTER the second roll = 100%

The odds that Jack will stop on the first roll = 1/2
The odds that Jack will stop on the first roll = 1/2 (getting an odd first) * 1/2 (getting an even next, so the sum is still odd) = 1/4

So the answer is 1/4 (That's what's left after we add 1/2 + 1/4).

Hope that helps!

-t

[anik1989]

thank you

[anik1989]

would you please more simplify with numeric entry?

[tommywallach]

I don't know what that means.

[anik1989]

would you please more simplify the ans. it stills ambiguous to me

[tommywallach]

Hey Anik,

I still don't know what you mean. I explained the question. If there's some part of it that doesn't make sense to you, I'm very happy to go into detail. However, I can't "simplify the answer." The answer is the answer. It can't be simplified. If you mean my explanation, I promise it's as simple as it can be. Please do let me know if there's a particular part of it that doesn't make sense to you, and explain why it doesn't make sense. Consider writing longer messages to better explain where you're coming from.

Thanks,

-t