altered die problem (Probability)

[bobsz]

Hello everyone,

I need some help with the following prob:

A bag contains 3 dice, 2 fair and 1 altered with all odd numbers replace with "1". One die is randomly selected and rolled independently twice. If the outcomes of both rolls were "1" and "1", what is the prob that the selected die is the altered die?

Thanks

[CRGreathouse]

What have you done?

[HallsofIvy]

What is the probability of rolling "1" two times in a row with a regular die? What is the probability of rolling "1" two times in a row with an altered die?

[bobsz]

Here's what I've done:

Let A= Altered die and B=outcome is 1

then P(A|B) = P(A∩B)/ P(B)
P(A∩B) = 1/12 ( outcome of 3 11's)
P(B)= 5/9 ( total outcome of 1's)

therefore P(A|B) = (1/12)/(5/9) = 3/20

Is this correct? Is there another way to approach this problem?

Thanks!