Question

If the odds in favour of an event be $\frac{3}{5}$, then the probability of the occurrence of the event is

• A. $\frac{5}{3}$
• B. $\frac{3}{8}$
• C. $\frac{5}{8}$
• D. $\frac{7}{8}$

Answer 1

The correct option is B $\frac{3}{8}$

Let the given event be E.
∴ Probability of the occurrence of event E = P(E)
Odds in favour of E $=\frac{3}{5}$
$\Rightarrow \frac{P\left(E\right)}{P\left(\overline{E}\right)}=\frac{3}{5}\Rightarrow \frac{P\left(E\right)}{1-P\left(E\right)}=\frac{3}{5}$
⇒ 5 P(E) = 3 – 3P(E)
⇒ 5 P(E) + 3 P(E) = 3
⇒ 8 P(E) = 3
$\therefore P\left(E\right)=\frac{3}{8}$

So, option b is correct.