Question

The odds against a certain event are $5:2$ and the odds in favour of another independent event are $6:5$. The probability that at least one of the events will happen, is

• A. $\frac{25}{77}$
• B. $\frac{52}{77}$
• C. $\frac{12}{77}$
• D. $\frac{65}{77}$

Answer 1

Answer: (B)

$\frac{52}{77}$

Let $A$ and $B$ are two given events
$\therefore$ $P\left(A\right)=\frac{2}{7},P\left(B\right)=\frac{6}{11}$
$\therefore$ Required probability $=1-P\left(\overline{A}\right)P\left(\overline{B}\right)$
$1-(1-\frac{2}{7})(1-\frac{6}{11})$
$=\frac{52}{77}$