# DBT JRF 2022 — Question 21

Exam: DBT JRF 2022 · Section: A · Topic: Aptitude › Probability · Difficulty: Medium

## Question

The probability that 1st of January is a Sunday in at least one of the 3 randomly chosen years is given by:

## Options

- **A.** $\frac{3}{7}$
- **B.** $1 - \left(\frac{6}{7}\right)^3$
- **C.** $\left(\frac{3}{7}\right)^3$
- **D.** $\left(1 - \frac{3}{7}\right)^3$

## Answer

Option B

## Explanation

Probability that January 1st is a Sunday in at least one of 3 years: Probability that Jan 1 falls on a Sunday in any single year = $\frac{1}{7}$ (equally likely for any day). Probability it does NOT fall on Sunday = $1 - \frac{1}{7} = \frac{6}{7}$ Using the complement rule: $P(\text{Sunday in at least one of 3 years}) = 1 - P(\text{not Sunday in ALL 3 years})$ $= 1 - \left(\frac{6}{7}\right)^3 = 1 - \frac{216}{343} = \frac{127}{343} \approx 0.370$ Answer: $1 - \left(\dfrac{6}{7}\right)^3$ (Option 2).

Source: https://mypyqbuddy.com/questions/the-probability-that-1st-of-january-is-a-6a104cd5920734408bc0c6f2