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 six 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?
A. 1/4 B. 3/8 C. 3/4 D. 1/2
GATE 2022 · General Aptitude · Probability · medium
Answer: P(both dice show only Q, U or V) = 1/4
Probability per die landing in {Q, U, V}: Each die has 6 equally likely faces. Three faces belong to {Q, U, V}. P(one die in {Q,U,V}) = 3/6 = 1/2
Apply independence: multiply probabilities for both dice: P(both dice in {Q,U,V}) = P(die 1 in {Q,U,V}) * P(die 2 in {Q,U,V}) = 1/2 * 1/2 = 1/4