NIMCET 2017 — Mathematics PYQ

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Question

NIMCET 2017 — Mathematics PYQ

NIMCET | Mathematics | 2017

A man is known to speak the truth 2 out of 3 times. He threw a dice cube with 1 to 6 on its faces andreports that it is 1. Then the probability that it is actually 1 is

Choose the correct answer:

Explanation

Calculation

Given, A man is known to speak the truth 2 out of 3 times.
A : Probability that man speaks the truth=P(A)= $\frac{2}{3}$
A' : The probability that man lies=P(A')= $\frac{1}{3}$
B : Probability of getting as 1on die face=P(B)= $\frac{1}{6}$
B' : Probability of not getting as 1on die face=P(B')= $\frac{5}{6}$

To find The probability that it is actually 1, Applying Baye's theorem, we get
$P (A ∣ B) = \frac{P ( A ) P ( B ∣ A )}{P ( A ) P ( B ∣ A ) + P ( n o t A ) P ( B ∣ n o t A )}$

$P (A ∣ B) = x = \frac{- b \pm b ^{2} - 4 a c}{2 a}$