Question

$A$ speak truth $0.6$, B speaks truth $0.7$. The probability of both contradicting each other is.......

• A. $0.46$
• B. $0.54$
• C. $0.72$
• D. $0.99$

Answer 1

Answer: (A)

$0.46$

Let $A=$ Event that A speaks the truth

$B=$ Event that B speaks the truth

Then $P\left(A\right)=0.6$

$P\left(B\right)=0.7$

$P\left(A^{\prime }\right)=1-0.6=0.4$

$P\left(B^{\prime }\right)=1-0.7=0.3$

Now

$A$ and $B$ contradict each other = [$A$ lies and $B$ true] or [$B$ true and $B$ lies]

$=P\left(A\right).P\left(B^{\prime }\right)+P\left(A^{\prime }\right).P\left(B\right)⟹0.6\times 0.3+0.4\times 0.7=0.46$