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There are two identical dice with a single letter on each of the faces. The following six letters: Q, R, S, T, U, and V, one on each of the faces. Any of the six outcomes are equally likely. The two dice are thrown once independently at random. What is the probability that the outcomes on the dice were composed only of any combination of the following possible outcomes: Q, U and V ?

There are two identical dice with a single letter on each of the faces. The following six letters: Q, R, S, T, U, and V, one on each of the faces. Any of the six outcomes are equally likely. The two dice are thrown once independently at random. What is the probability that the outcomes on the dice were composed only of any combination of the following possible outcomes: Q, U and V ? Correct Answer 1/4

Given:

There are two identical dice with a single letter on each of the faces: Q, R, S, T, U, V

Formula used:

Probability of outcomes = Total number of favorable outcomes/Total number of possible outcomes

Calculation:

Total faces of each dice = 6

We know that in a single thrown of two dice, the number of possible outcomes = 6 × 6 = 36

Favorable outcomes can be composed of any combination of Q, U, and V are (Q, Q), (U, U), (V, V), (Q, U), (U, Q), (Q, V), (V, Q), (U, V), (V, U).

There are three favorable outcomes that come from each dice.

Total numbers of favorable outcomes can be composed of any combination of Q, U, and V = 9

∴ The probability that the outcomes on the dice can be composed of any combination of Q, U, and V = 9/36 = 1/4

∴ The probability that the outcomes on the dice were composed only of any combination of the following possible outcomes: Q, U, and V are 1/4.

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