JEE Main 2023MathematicsProbabilityHardMCQ

JEE Main 2023 — Probability Question with Solution

JEE Main 2023 (31 Jan Shift 1)

Question

A bag contains 6 balls. Two balls are drawn from it at random and both are found to be black. The probability that the bag contains at least 5 black balls is

Choose an option

Show full solutionCorrect option: A
Correct answer
A57

Step-by-step explanation

Let the bag contains black ballsB and non-black balls B¯, then we can have the following possibilities:

6B,0B¯, 5B,1B¯, 4B,2B¯, 3B,3B¯,2B,4B¯

All the events are equally likely, i.e., 15.

Required probability

=15×C26C26+15×C25C2615×C26C26+15×C25C26+15×C24C26+15×C23C26+15×C22C26

=2535=57

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About this question

This is a previous-year question from JEE Main 2023, covering the Probability chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.