Probability mass function question. Why is the answer 3/7

[cloud360]

Homework Statement

Consider the following situation. You toss a coin three times and count the total number of heads,
Y . You then roll a die and record the score, X. Finally, calculate Z = Y × X, that is, the total
number of heads multiplied by the score on the die.

(b) Find the probability that Y = 1 given that Z = 6.

Homework Equations

n/a

The Attempt at a Solution

I have got the solution. But don't know why it is. Why is the answer to B =3/7

I think it should be probability that y=1, which is 3/8...divide by probability Z=6...which is 7/48


therfore answer is=18/7...which is know is impossible
[PLAIN]http://img713.imageshack.us/img713/2558/pmfk.png
http://img713.imageshack.us/img713/2558/pmfk.png

 

[cloud360]

to get z=6, where y=1...x must be 6

as 6*1=6...(the 1 represents y)

probability x=6...is 1/6

it is 1*6

 

[hgfalling]

They want to know:

GIVEN that Z is 6, what is the chance that Y is 1.

So we already know that Z was 6. So our whole universe of possible outcomes is therefore restricted to Z=6. So what are the possible outcomes and their relative probabilities? Write them down. Then look at how often among the restricted universe that Y=1.