Skip to content
GATEiit

GATE CSE 2021 Set 2 Q43: Pólya urn: probability of red on the fourth draw

Question

A bag has rr red balls and bb black balls. All balls are identical except for their colours. In a trial, a ball is randomly drawn from the bag, its colour is noted and the ball is placed back into the bag along with another ball of the same colour. Note that the number of balls in the bag will increase by one, after the trial. A sequence of four such trials is conducted. Which one of the following choices gives the probability of drawing a red ball in the fourth trial?

Try it: multiple choice: exactly one correct option

Select one option
Wrong answer costs 2/3 mark in GATE.
Show answer and explanation

Answer: A (official GATE 2021 final answer key)

Concept used: In a Pólya urn the probability of red on any single draw stays equal to the initial proportion.

First step: Check the second draw by total probability: rr+b⋅r+1r+b+1+br+b⋅rr+b+1\frac{r}{r+b}\cdot\frac{r+1}{r+b+1} + \frac{b}{r+b}\cdot\frac{r}{r+b+1}, and simplify.

Full step-by-step solution

Detailed working, common mistakes and linked mock tests will be available with a free GATEiit account. Log-in is coming soon.

Share this question

WhatsAppDownload image

Source: official GATE 2021 Set 2 CS question paper and final answer key, organised by IIT Bombay. Question paper · Answer key

More Engineering Mathematics PYQs

PracticePractise Engineering Mathematics questions →Full paperAll GATE CSE 2021 Set 2 questions →