p40 in Guo Manual Problem 6

"You first toss a coin. If you get heads, then you throw a die; if you get tails, then you toss another coin"

Find

(3) The probability that you get heads and the number 6

I thought the answer would be 1/12, since the probability you get heads is 1/2, so (H,1)+(H,2)+(H,3)+(H,4)+(H,5)+(H,6)=1/2, so each one being equally likely, they would each have a probability of 1/12.

But the manual says the probability is 1/8, since there are 8 possible outcomes, and they are all equally likely.

Is this correct?

If so, how does it relate to all the heads outcomes adding up to 1/2?

"You first toss a coin. If you get heads, then you throw a die; if you get tails, then you toss another coin"

Find

(3) The probability that you get heads and the number 6

I thought the answer would be 1/12, since the probability you get heads is 1/2, so (H,1)+(H,2)+(H,3)+(H,4)+(H,5)+(H,6)=1/2, so each one being equally likely, they would each have a probability of 1/12.

But the manual says the probability is 1/8, since there are 8 possible outcomes, and they are all equally likely.

Is this correct?

If so, how does it relate to all the heads outcomes adding up to 1/2?

## Comment