JEE Main 2022MathematicsProbabilityEasyMCQ

JEE Main 2022 — Probability Question with Solution

JEE Main 2022 (24 Jun Shift 1)

Question

If a random variable X follows the Binomial distribution B33,p such that 3PX=0=PX=1, then the value of PX=15PX=18-PX=16PX=17 is equal to

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Show full solutionCorrect option: A
Correct answer
A1320

Step-by-step explanation

We know that p=success, q=failure

Given 3PX=0=PX=1

3C033p0q33=C133p1q32

3×1×q=33×p

q=11p   ... i

Also p+q=1

Now from equation i, p+11p=1

12p=1

p=112, q=1112

Now PX=15PX=18-PX=16PX=17

⇒C1533p15q18C1833p18q15-C1633p16q17C1733p17q16

=q3p3-qp=qpqp2-1=111112-1

=11×120

=1320

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About this question

This is a previous-year question from JEE Main 2022, 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.