Suppose you roll three dice at once each with four faces lab

Suppose you roll three dice at once, each with four faces labelled 1, 2, 3, and 4.

A)What is the probability that all three dice will show the same number?

B) What is the probability that all three dice will show different numbers? (i.e., that no two dice show the same number?)

Solution

There are a total of 4*4*4 = 64 outcomes for the three dice.

A.

There are only 4 possible outcomes for this, that is, all 1\'s, all 2\'s, all 3\'s, and all 4\'s.

Thus, the probability is 4/64 = 1/16 = 0.0625. [ANSWER]

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B.

Order matters here, that is, which die showed what number.

Thus, we use permutation.

There are 4P3 ways = 24 ways to do this.

Thus, the probability is 24/64 = 3/8 = 0.375 [ANSWER]