Question

A speaks truth 6 out of 10 and B speaks truth 4 out of 10 times. What is the probability of them contradicting each other?

• A. 0.52
• B. 0.55
• C. 0.48
• D. 0.09

Answer 1

Answer: (A)

0.52

Given,

Probability that A speak truth $P\left(a\right)=0.6$

Probability that A does not speak truth $P^{\prime }\left(a\right)=1-P\left(a\right)=1-0.6=0.4$

Probability that B speak truth $P\left(b\right)=0.4$

Probability that B does not speak truth $P^{\prime }\left(b\right)=1-P\left(b\right)=1-0.4=0.6$

Probability that A and B contradict each other

$=P\left(a\right).P^{\prime }\left(b\right)+P^{\prime }\left(a\right).P\left(b\right)\to =0.6\times 0.6+0.4\times 0.4\to =0.36+0.12=0.52$