Exercise 12.22. Yahtzee. In a dice game, a "Yahtzee" is a result in which all five dice within a ...

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Exercise 12.22. Yahtzee. In a dice game, a Yahtzee is a result in which all five dice within a round have the same value. T

math Statistics-And-Probability

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Answer 1

Answer #1

The probability of getting a Yahtzee in one round is first computed as:

There are a total of 6⁵ possibilities in a throw of 5 dice and the number of ways a Yahtzee could be obtained is when all show the same face (one of the 6 faces ) so 6 ways. Therefore probability of getting a yahtzee in one round is computed as: 6/6⁵ = 1/6⁴

Now for 3 independent rounds, the total number of times he gets a yahtzee could be modelled as a binomial distribution such that:

$X \sim Bin(n = 3, p = \frac{1}{6^4})$

Now the variance for the above binomial distribution could be obtained easily as:

$V(X) = pn(1-p) = \frac{3}{6^4}(1- \frac{1}{6^4}) = 0.002313$

Therefore 0.002313 is the required variance here.

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