Four sided die rolled twice problem.

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In summary, the problem involves rolling a four-sided die twice and recording the scores on each roll. The sample space for this experiment is 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)}. In part (b), X is defined as the larger of the two outcomes if they are different, and the common value if they are the same. The probability table for X can be obtained by determining the value of X for each point in S and calculating the probability for
  • #1
M1ZeN
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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
 
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  • #2
M1ZeN said:

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
 
  • #3
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.
 

1. What is the probability of rolling a specific number on a four-sided die?

The probability of rolling a specific number on a four-sided die is 1/4 or 25%, since there are four possible outcomes (1, 2, 3, or 4) and one of them will result in the desired number.

2. What is the probability of rolling the same number twice on a four-sided die?

The probability of rolling the same number twice on a four-sided die is 1/16 or 6.25%, since there are four possible outcomes for the first roll and only one of those outcomes will result in the same number on the second roll.

3. What is the probability of rolling a higher number on the second roll compared to the first roll on a four-sided die?

The probability of rolling a higher number on the second roll compared to the first roll on a four-sided die is 3/8 or 37.5%, since there are three possible outcomes (3, 4, or higher) for the second roll that will result in a higher number, out of a total of eight possible outcomes (4 possible outcomes for the first roll multiplied by 2 possible outcomes for the second roll).

4. What is the expected value for the sum of two rolls on a four-sided die?

The expected value for the sum of two rolls on a four-sided die is 5, since each roll has an equal chance of resulting in any of the four numbers (1, 2, 3, or 4) and the sum of these numbers is 5. Therefore, the expected value is calculated as (1+2+3+4)/4 = 5.

5. How does the probability of obtaining a specific combination of numbers on two rolls of a four-sided die change if the die is rolled more than two times?

The probability of obtaining a specific combination of numbers on two rolls of a four-sided die remains the same regardless of how many times the die is rolled. This is because each roll is an independent event and the probability for each roll does not change. However, the overall probability of obtaining a specific combination of numbers may increase with more rolls, as there are more opportunities for the desired outcome to occur.

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