Four sided die rolled twice problem.

[M1ZeN]

Homework Statement

A four-sided die is rolled twice and the scores (1, 2, 3 or 4) recorded on each roll.
(a) What is the sample space for this experiment?
(b) Let X equal the larger of the two outcomes if they are different and the common value if they are the same. Write down the probability table for x.
(c) Find a formula for the probability (mass) function, (p.m.f.), f(x).

Homework Equations

Not sure.

The Attempt at a Solution

I know Part (A).

S = {(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(2,4),( 3,1),(3,2),(3,3),(3,4),(4,1),(4,2),(4,3),(4,4)}

I'm not sure of what there asking for Part (B). Would X be everywhere there is 3 and 4 both when its different [(3,4)?] and when they are same [(3,3) & (4,4)?]?

Part (C) I'm not sure of also but I know it would be some formula including X and the denominator being 16.

Thanks

 

[Ray Vickson]

Homework Statement

A four-sided die is rolled twice and the scores (1, 2, 3 or 4) recorded on each roll.
(a) What is the sample space for this experiment?
(b) Let X equal the larger of the two outcomes if they are different and the common value if they are the same. Write down the probability table for x.
(c) Find a formula for the probability (mass) function, (p.m.f.), f(x).

Homework Equations

Not sure.

The Attempt at a Solution

I know Part (A).

S = {(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(2,4),( 3,1),(3,2),(3,3),(3,4),(4,1),(4,2),(4,3),(4,4)}

I'm not sure of what there asking for Part (B). Would X be everywhere there is 3 and 4 both when its different [(3,4)?] and when they are same [(3,3) & (4,4)?]?

Part (C) I'm not sure of also but I know it would be some formula including X and the denominator being 16.

Thanks

In (b), what is stopping you from writing the value of X for each point in S? If you know the probability of each point in S, can you see how to get the probabilities for the various values of X? That leads directly to the solution of (c).

RGV

 

[M1ZeN]

I'm just not understanding specifically what there asking for in Part B. Call me stupid, its just the way the question is worded I'm not getting what to look for.