JEE Main 2021MathematicsProbabilityEasyMCQ

JEE Main 2021 — Probability Question with Solution

JEE Main 2021 (27 Jul Shift 2)

Question

A student appeared in an examination consisting of 8 true-false type questions. The student guesses the answers with equal probability. The smallest value of n, so that the probability of guessing at least n correct answers is less than 12, is :

Choose an option

Show full solutionCorrect option: A
Correct answer
A5

Step-by-step explanation

PE<12

⇒∑r=n8Cr8128-r12r<12

⇒∑r=n8Cr8128<12

⇒Cn8+Cn+18+…+C88<128

⇒256-C08+C18+…+Cn-18<128

⇒C08+C18+…+Cn-18>128

⇒1+8+28+56+70+C58+…+Cn-18>128

⇒163+C58+…+Cn-18>128

⇒n-1≥4

⇒n≥5

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Probability chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.

Solve interactively →

About this question

This is a previous-year question from JEE Main 2021, 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.