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 atleast 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

The correct option is B

$\frac{52}{77}$

Explanation for the correct option

We know that,

$\mathrm{Probability}\mathrm{of}\mathrm{an}\mathrm{even}=\frac{\mathrm{Number}\mathrm{of}\mathrm{favourable}\mathrm{outcome}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes}}$

Odds in favour of certain event $=2:5$

Therefore probability of happening$=\frac{2}{7}$

Therefore probability of not happening$=1-\frac{2}{7}=\frac{5}{7}$

Odds in favour of another event $=6:5$

Probability of happening $=\frac{6}{11}$

Therefore probability of not happening$=1-\frac{6}{11}=\frac{5}{11}$

Therefore, the required probability$=1-\mathrm{none}\mathrm{of}\mathrm{the}\mathrm{event}\mathrm{happens}$

$$\begin{gathered} =1-\left[\frac{5}{7}·\frac{5}{11}\right] \\ =1-\frac{25}{77} \\ =\frac{52}{77} \end{gathered}$$

Hence, the correct option is $\left(\mathrm{B}\right)$