JEE Main 2021 — Probability Question with Solution
From: JEE Main 2021 (Online) 24th February Morning Shift
Question
Let Bi (i = 1, 2, 3) be three independent events in a sample space. The probability that only B1 occur is , only B2 occurs is and only B3 occurs is . Let p be the probability that none of the events Bi occurs and these 4 probabilities satisfy the equations and (All the probabilities are assumed to lie in the interval (0, 1)).
Then is equal to ________.
Then is equal to ________.
Enter your answer
Show full solutionCorrect answer: 6
Correct answer
6
Step-by-step explanation
Let x, y, z be probability of B1, B2, B3 respectively
= P(B1 ) =
x(1 y)(1 z) =
Similarly, y(1 x)(1 z) =
z(1 x)(1 y) =
and (1 x)(1 y)(1 z) = p
( 2)p =
(x(1 y)(1 z) 2y(1 x)(1 z)) (1 x)(1 y)(1 z) = xy(1 x)(1 y)(1 z)
x xy 2y + 2xy = xy
x = 2y ...... (1)
Similarly ( 3)p = 2
y = 3z .... (2)
From (1) & (2)
x = 6z
Now
= P(B1 ) =
x(1 y)(1 z) =
Similarly, y(1 x)(1 z) =
z(1 x)(1 y) =
and (1 x)(1 y)(1 z) = p
( 2)p =
(x(1 y)(1 z) 2y(1 x)(1 z)) (1 x)(1 y)(1 z) = xy(1 x)(1 y)(1 z)
x xy 2y + 2xy = xy
x = 2y ...... (1)
Similarly ( 3)p = 2
y = 3z .... (2)
From (1) & (2)
x = 6z
Now
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