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 $=1-P(\overline{A})P(\overline{B})$ $=1-\left(1-\frac{2}{7}\right)\left(1-\frac{6}{11}\right)$ $=1-\frac{5}{7}\times \frac{5}{11}=\frac{52}{77}$