A pair of dice is rolled, and the number that appears uppermost on each die is observed. Refer to this experiment and find the probability of the given event. (Enter your answer as a fraction.)
One die shows a 5, and the other is a number less than 4.

Question

A pair of dice is rolled, and the number that appears uppermost on each die is observed. Refer to this experiment and find the probability of the given event. (Enter your answer as a fraction.)
 One die shows a 5, and the other is a number less than 4.

anonymous · Answer

The roll of the dice (suppose one red, one green) are independent of one another.  First, we want to get a five on the red die, which is a one out of six chance. Then we need to get a number less than four on the green die, which is a 1/2 probability.  Multiply to get a 1/12 probability.   Now, we realize that we might also get the same results with a five on the green die, and a small number on the red.  So the overall probability is 1/6.

anonymous · Answer

I concede that the explanation might be circuitous, but I'm pretty sure the answer is correct.

anonymous · Answer

thankss!!

anonymous · Answer

You could list the sample space and count just as fast as figuring it out, also.  That's how I checked my argument.