A fair four-sided dice, numbered 1, 2, 3, and 4 is rolled twice. If the score on

Question

A fair four-sided dice, numbered 1, 2, 3, and 4 is rolled twice. If the score on the 2nd roll is strictly greater than the score on the first roll, then the player wins the difference in dollars. If the score on the second roll is strictly less than the score on the 1st roll, then the player loses the difference in dollars. If the scores are equal, the player neither wins nor loses. If we let X denote the (possibly negative) winnings of the player, what is the probability mass function of X? (Note that X can take any of the values from {-3, -2, 1, 0, 1, 2, 3}).

Explanation / Answer

The following table provides the event space for X: Winnings of the player.

Event space for X=-3

P(X=-3) = Number of events favoring X=-3 / Total number events =1/16

Similarly event space for X=-2

P(X=-2) = Number of events favoring X=-2 / Total number events =2/16=1/8

Similarly event space for X=-1

P(X=-1) = Number of events favoring X=-1 / Total number events =3/16

Similarly event space for X=0

P(X=0) = Number of events favoring X=0 / Total number events =4/16=1/4

Similarly event space for X=1

P(X=1) = Number of events favoring X=1 / Total number events =3/16

Similarly event space for X=2

P(X=2) = Number of events favoring X=2 / Total number events =2/16=1/8

Event space for X=3

P(X=3) = Number of events favoring X=3 / Total number events =1/16

So, the probability mass function of X:

Event Number Dice1 Dice2 X: Dice 2 -Dice1 1 1 1 0 2 1 2 -1 3 1 3 -2 4 1 4 -3 5 2 1 1 6 2 2 0 7 2 3 -1 8 2 4 -2 9 3 1 2 10 3 2 1 11 3 3 0 12 3 4 -1 13 4 1 3 14 4 2 2 15 4 3 1 16 4 4 0

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.