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)

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