# Dice probability

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1. Jul 31, 2016

### Mark53

1. The problem statement, all variables and given/known data

In a probability experiment, a fair die is rolled twice.
• If the first roll is odd, the outcomes are recorded as they appear.
• If the first roll is even, the recorded outcome for the second die is doubled. For example, if the first die was 2 and the second 4, the recorded outcome would be (2,8).

Let A be the event that the first recorded outcome is even and B be the event that the second is even.

(a) Write down the sample space S for this experiment.
(b) Express A, B and A∩B as subsets of S.
(c) Find P(A) and P(B).
(d) Given that the second recorded outcome is even, what is the probability that the first roll was also even?

3. The attempt at a solution

I am not sure if the the numbers that I have used below are correct any help is much appreciated

a)
s={(2,4),(2,8),(2,12),(4,4),(4,8),(4,12),(6,4),(6,8),(6,12)}

b)

A={2,4,6}
B={4,8,12}
A∩B = {4}

c)

P(A)=1/2
P(B)=1/2

d)

P=1/4

2. Jul 31, 2016

### Orodruin

Staff Emeritus
This set is far from complete. What happened to all of the cases where either the first or second die gave 1, 3, or 5?
These are not subsets of your S.

3. Jul 31, 2016

### Mark53

S={(2,2),(2,4),(2,6),(2,8),(2,10),(2,12),(4,2)(4,4),(4,6),(4,8),(4,10),(4,12),(6,2),(6,4),(6,6),(6,8),(6,10),(6,12),(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(3,1),(3,2),(3,3),(3,4),(3,5)(3,6),(5,1),(5,2),(5,3)(5,4),(5,5),(5,6)}

A={(2,2),(2,4),(2,6),(2,8),(2,10),(2,12),(4,2)(4,4),(4,6),(4,8),(4,10),(4,12),(6,2),(6,4),(6,6),(6,8),(6,10),(6,12)}

B={(2,2),(2,4),(2,6),(2,8),(2,10),(2,12),(4,2)(4,4),(4,6),(4,8),(4,10),(4,12),(6,2),(6,4),(6,6),(6,8),(6,10),(6,12),(1,2),(1,4),(1,6),(3,2),(3,4),(3,6),(5,2),(5,4),(5,6)}

A∩B = {(2,2),(2,4),(2,6),(2,8),(2,10),(2,12),(4,2)(4,4),(4,6),(4,8),(4,10),(4,12),(6,2),(6,4),(6,6),(6,8),(6,10),(6,12)}

P(A)=1/2
P(B)=3/4

d)
P=1/2

Would this be correct now

4. Jul 31, 2016

### PeroK

a) - c) are correct. How did you calculate d)?

5. Jul 31, 2016

### Mark53

I used A∩B how should I be calculating it?

6. Jul 31, 2016

### PeroK

$P(A \cap B)$ is the probability that both are even. The probability that the first is even given that you know the second is even is something else. Can you see that?

7. Jul 31, 2016

### Mark53

Does that mean that it is 1/4 I am still unsure

8. Jul 31, 2016

### PeroK

9. Jul 31, 2016

### Mark53

10. Jul 31, 2016

Yes.