JEE Main 2024MathematicsProbabilityMediumMCQ

JEE Main 2024 — Probability Question with Solution

JEE Main 2024 (31 Jan Shift 1)

Question

Three rotten apples are accidently mixed with fifteen good apples. Assuming the random variable x to be the number of rotten apples in a draw of two apples, the variance of x is

Choose an option

Show full solutionCorrect option: D
Correct answer
D40153

Step-by-step explanation

Given apples are: 3 bad, 15 good

Let X be no. of bad apples.

⇒PX=0=15C218C2=15!2!×13!18!2!×16!

⇒PX=0=15×1418×17=5×73×17

⇒PX=0=3551

⇒PX=1=3C1×15C118C2=3×159×17

⇒PX=1=517

⇒PX=2=3C218C2=39×17

⇒PX=2=3153

⇒EX=0×3551+1×517+2×3153

⇒EX=13

We know that, VarX=EX2−EX2

⇒VarX=0×3551+1×517+4×151−132

⇒VarX=1951−19

⇒VarX=40153

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About this question

This is a previous-year question from JEE Main 2024, 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.