probability question, please help

[maria08]

A fair 6-sided die is rolled twice.

Quantity A
The probability of rolling the same number both times.

Quantity B
The probability of rolling two different even numbers.

My reasoning told me that Quantity A should be 1/6 x 1/6 = 1/36
and
Quantity B:
We've got 2 different even numbers in a die - 2,4 and 6.
The probability of getting one of these in the first roll would be 3/6 and then the probability of getting a second one (different from the first one) would be 2/6. Thus 6/36 or 1/6.

Answer: C (both equal)
Can someone point out if my reasoning is correct and whether there is a shortcut to solving this on the test day.

many thanks :)

[tommywallach]

Hey Lore,

Be very careful on the GRE in general of using "reasoning" instead of math. Instead, use process.

Probability process.

1. Figure out # of events
2. Figure out individual probability of each event
3. If you need all of them to happen, multiply them together; if you're happy with one or another thing happening, add them.

Quantity A:

1. There are two events
2. a. The probability of getting what we need on the first toss is 100%, because it's okay to get ANY of the six numbers.
b. The probability of getting the SAME number on the second toss is 1/6.
3. We need both things to happen, so we multiply: 1 * 1/6 = 1/6

Quantity B
1. There are two events.
2. a. The probability of getting an even number first is 3/6=1/2
b. The probability of getting a different even number second is 2/6 = 1/3
3. We need both to happen, so multiply: 1/2 * 1/3 = 1/6

Hope that helps!

-t

[maria08]

Thanks Tommy

In reality I tend to get intimidated by probability questions and no doubt I need more practice to gain confidence on the test day.
I've done all the probability questions from the 5lb book - apart from the MGRE tests that are still due for me, is there any further practice on probability that you can recommend?

cheers :)

[tommywallach]

Hey Lore,

I definitely don't think people need more material than the basic books, the Official Guide to the GRE, and the 5lb book. I don't know of any other books I would recommend, but I also wouldn't worry about it. You might see one probability question on the real GRE. Hopefully you'll get it right. If you don't, it still isn't going to tank your score. : )

-t