Probability Question from GmatPrep Test

[onlyGmat2008]

Hello,

I am not able to solve the problem (attached).

Could you please help me with this?

Thanks.

[VP_Tatiana]

Ok, so we have 15 slate rocks out of 45 rocks total.

The first time we pick a rock, we have a 15/45 = 1/3 chance of getting a slate rock.

Since we are not replacing that rock, we now have 14 slate rocks and 44 rocks total, for a 14/44 = 7/22 chance of getting a slate rock.

In order to get two slate rocks, we need to be in the lucky 1/3 that get a slate rock the first time, and then in the lucky 7/22 that get a slate rock the second time. To calculate the probability of being lucky both times, we need to multiply these outcomes together.

1/3 * 7/22 = 7/66

Hope that helps,

Tatiana

[onlyGmat2008]

Thank You so much.

[manu217]

Thank you for your reply. However could you please clarify why did you multiply 1/3 and 7/22 and not add the probabilities?
Thanks