Question

The probability that A speaks truth is $\frac{4}{5}$, while this probability for B is $\frac{3}{5}$. The probability of at least one of them is true when asked to speak on an event is ___________.

• A. $\frac{3}{25}$
• B. $\frac{2}{25}$
• C. $\frac{23}{25}$
• D. $\frac{4}{25}$

Answer 1

The correct option is C $\frac{23}{25}$

Given, probability of A speaking truth $P\left(A\right)=\frac{4}{5}$

probability of A doesn't speak truth $P\left(A1\right)=1-P\left(A\right)=1-\frac{4}{5}=\frac{1}{5}$

probability of B speaking truth $P\left(B\right)=\frac{3}{5}$

probability of B doesn't speak truth $P\left(B1\right)=1-P\left(B\right)=1-\frac{3}{5}=\frac{2}{5}$

probability of at least one of them is true = 1 - (probability of no one speaks true)

$=1-P\left(A1\right)P\left(B1\right)=1-\left(\frac{1}{5}\right)\left(\frac{2}{5}\right)$

$=\frac{25-2}{25}=\frac{23}{25}$