The GATE Grind

GATE 2022 EE – Question 7

General Aptitude · Quantitative Aptitude: Probability and Combinatorics · 2 marks · Multiple choice

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?

  1. $\frac14$
  2. $\frac34$
  3. $\frac16$
  4. $\frac{5}{36}$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) $\frac14$

Explanation

Each die shows one of Q, U, V with probability $\frac36=\frac12$. For both dice independently, the probability is $\frac12\times\frac12=\frac14$.