The probabilities that A and B will tell the truth are 2 / 3 and 4 / 5 respectively . What is the probability that they agree with each other ?
Solution
Correct Answer: Option A
Let A be the event of A will tell truth. B be the event of B tell truth
\(P(A)=\frac23,P(A^c)=1-P(A)=\frac13\)
\(P(B)=\frac45,P(B^c)=1-P(B)=\frac15\)
When both agree then they say true or they say false together, that is
\(A\cap B\;or\;A^c\cap B^c\)
Also these events will be mutually exclusive :
\(P(A\cap B)+P(A^c\cap B^c)=P(A)P(B)P(C)=\frac23\times\frac45+\frac13\times\frac15=\frac35\)
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