JEE Main 2017MathematicsProbabilityMediumMCQ

JEE Main 2017 — Probability Question with Solution

JEE Main 2017 (02 Apr)

Question

For three events, A, B and C, P(Exactly one of A or B occurs)

=P(Exactly one of B or C occurs)

=P(Exactly one of C or A occurs) =14 and P(All the three events occur simultaneously) =116.

Then the probability that at least one of the events occurs, is:

Choose an option

Show full solutionCorrect option: B
Correct answer
B716

Step-by-step explanation

a=116

c+d+e+f=14   ...i

b+d+e+g=14   .....ii

b+f+c+g=14   ....iii

Adding i, ii and iii

⇒ 2b+c+d+e+f+g=34

⇒ b+c+d+e+f+g=38

Now ⇒ PA∪B∪C=a+b+c+d+e+f+g

⇒ PA∪B∪C=116+38

⇒ PA∪B∪C=716

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About this question

This is a previous-year question from JEE Main 2017, 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.