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, because 1/2 the time you get heads, so (heads,roll1)+(heads,roll2)+(heads,roll2)+(heads,r oll2)+(heads,roll2)+(heads,roll2)=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.

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, because 1/2 the time you get heads, so (heads,roll1)+(heads,roll2)+(heads,roll2)+(heads,r oll2)+(heads,roll2)+(heads,roll2)=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.

Is this correct?

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

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