JEE Main 2020 — Probability Question with Solution
From: JEE Main 2020 (Online) 6th September Evening Slot
Question
The probabilities of three events A, B and C are
given by
P(A) = 0.6, P(B) = 0.4 and P(C) = 0.5.
If P(AB) = 0.8, P(AC) = 0.3, P(ABC) = 0.2, P(BC) =
and P(ABC) = , where 0.85 0.95, then lies in the interval :
P(A) = 0.6, P(B) = 0.4 and P(C) = 0.5.
If P(AB) = 0.8, P(AC) = 0.3, P(ABC) = 0.2, P(BC) =
and P(ABC) = , where 0.85 0.95, then lies in the interval :
Choose an option
Show full solutionCorrect option: C
Correct answer
C[0.25, 0.35]
Step-by-step explanation
P(A B) = P(A) + P(B) – P(A B)
0.8 = 0.6 + 0.4 – P(A B)
P(A B) = 0.2
P(ABC) = P(A) + P(B) + P(C) – P(A B) – P(B C) –P(C A) + P(A B C)
= 0.6 + 0.4 + 0.5 - 0.2 - - 0.3 + 0.2
+ = 1.2
= 1.2 -
Given, 0.85 0.95
0.85 1.2 - 0.95
0.25 0.35
0.8 = 0.6 + 0.4 – P(A B)
P(A B) = 0.2
P(ABC) = P(A) + P(B) + P(C) – P(A B) – P(B C) –P(C A) + P(A B C)
= 0.6 + 0.4 + 0.5 - 0.2 - - 0.3 + 0.2
+ = 1.2
= 1.2 -
Given, 0.85 0.95
0.85 1.2 - 0.95
0.25 0.35
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This is a previous-year question from JEE Main 2020, 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.