The game of Yahtzee is played with five fair dice. The goal is to roll certain \

Question

The game of Yahtzee is played with five fair dice. The goal is to roll certain 'hands', such as Yahtzee (all five dice showing the same number) or a full house (three of a kind and two of a kind). In the first round of a player's turn, the player all five dice. Based on the outcome of that roll, the player has a second and round, where he/she can then choose to re-roll any subset of the dice to get rolls third a desired hand. (a) What is the probability of rolling a Yahtzee on the first round? (b) A small straight is defined as having 4 of the 5 dice all in a row (for example, {1,2,3, 4,6]). What is the probability of rolling a small straight on the first round?

Explanation / Answer

(a)
Probability of getting any number as outcome on rolling a die is 1/6

Probability of getting the same number as output on all 5 dice, (1/6)^5

As there are 6 possible outcomes any number can be appeared on all five dice i.e. 6C1 = 6 ways

Hence required probability of rolling a Yahtzee on the first round is 6 * (1/6)^5 = (1/6)^4 = 0.000772

(b)
Possible number of small straights are two as follows
{1,2,3,4,6}
{1,3,4,5,6}

Probability of rolling a small straight = 2C1/(6^5) = 2/(6^5) = 0.000257

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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