Question

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

• A. $ \frac{50}{77} $
• B. $ \frac{52}{77} $
• C. $ \frac{25}{88} $
• D. $ \frac{63}{88} $

Answer 1

Answer: (B)

Let $ =\frac{41}{161} $ and $ P(B)=\frac{6}{11} $ $ \therefore $ The required probability $ =1-P(\overline{A})P(\overline{B}) $ $ =1-\left( 1-\frac{2}{7} \right)\left( 1-\frac{6}{11} \right) $ $ =1-\frac{5}{7}\times \frac{5}{11}=\frac{52}{77} $