Question

'X' speaks truth in $60$ & 'y' is $50$ of the cases. The probability that they contradict each other while narrating the same incident, is

• A. $\frac{1}{2}$
• B. $\frac{1}{8}$
• C. $\frac{1}{4}$
• D. $\frac{2}{3}$

Answer 1

The correct option is A $\frac{1}{2}$

Given:

Probability of $X$ speaking truth, $P\left(X\right)=60\%=0.6$

Probability of $Y$ speaking truth, $P\left(Y\right)=50\%=0.5$

To find:

Probability of contradiction.

$P\left(X^{\prime }\right)=0.4,P\left(Y^{\prime }\right)=0.5$

Contradiction occurs when X speaks truth and Y speaks false or X speaks false and Y speaks truth. And as all the events are independent,

i.e.,, Required probability = $P(X\cap Y^{\prime })+P(X^{\prime }\cap Y)=P\left(X\right)\times P\left(Y^{\prime }\right)+P\left(X^{\prime }\right)\times P\left(Y\right)$

$⟹=0.6\times 0.5+0.4\times 0.5=0.3+0.2=0.5=\frac{1}{2}$