Suppose you roll a single, six-sided die with numbers 1 - 6 printed on the sides

Question

Suppose you roll a single, six-sided die with numbers 1 - 6 printed on the sides. Assume that each side has an equal probability of being rolled. Enter your probabilities as a decimal rounded to 3 decimal places or as a simplified fraction.

(a) Complete the probability distribution for the number showing on one roll of a die.

(b) What is the mean of the probability distribution?


(c) What is an accurate interpretation of this value?

It is the value of every single roll of a fair die.

It is the probability of rolling a 5.    

If you rolled a single die over and over, keeping track of the number showing on the die, then averaged all these values, you should get the value in part (b).

It is meaningless because you can never actually roll the value given in part (b).

x = # on the die          P(x)          1          ____ 2         ____ 3           _____ 4          ______ 5          ______ 6         ______

Explanation / Answer

a) P(X = 1) = 1/6 = 0.167

P(X = 2) = 1/6 = 0.167

P(X = 3) = 1/6 = 0.167

P(X = 4) = 1/6 = 0.167

P(X = 5) = 1/6 = 0.167

P(X = 6) = 1/6 = 0.167

b) Mean, E(X) = (1/6) * (1 + 2 + 3 + 4 + 5 + 6) = 3.5

c) Option-C) If you rolled a single die over and over, keeping track of the number showing on the die, then averaged all these values, you should get the value in part (b).

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