Question

Two number cubes are rolled- one blue and one yellow. Find the probability that the blue cube is less than 3 and the product is 8.

a) Is this event independent or dependent? Explain why.

b) Find the probability that the blue cube is less than 3 and the product is 8.

Answer 1

(Problem a) The events are dependent because you're looking for a specific product.

(Problem b) Now, assuming that the cubes have six faces:

P(blue is less than 3)= 2/6 = 1/3


The product is 8; 1*8=8, but there is no 8 on a die. So blue must be 2 and yellow must be 4; 2*4=8. Since there is a 1/6 chance for each die (Six faces per die), you multiply 1/6*1/6 = 1/36 chance.

Now add the P(blue is less than 3) = 1/3

1/36 + 1/3 = ?

1/36 + 12/36 = 13/36

Therefore, P(blue is less than 3 and the product is 8)= 13/36


Hope this helps :)