Question

If the probability of the occurrence of a certain event E is $\frac{5}{13}$ , then the odds against its occurrence is

• A.
  $\frac{8}{13}$
• B.
  $\frac{5}{8}$
• C.
  $\frac{5}{13}$
• D.
  $\frac{8}{5}$

Answer 1

The correct option is D

$\frac{8}{5}$
Given:

$P\left(E\right)=\frac{Numberoffavourableoutcomes}{Totalnumberofoutcomes}=\frac{5}{13}$

Here, the number of outcomes favourable to E will be the multiple of 5 say 5k and the total number of outcomes will be the multiple of 13 say 13k, where k is a natural number.

Thus, the total number of unfavourable outcomes $=13k–5k=8k.$

Now, odds against an event is given by number of unfavourable outcomes to the number of favourable outcomes.

$\therefore$ Odds against event $E=\frac{8k}{5k}=\frac{8}{5}$

Hence, the correct answer is option (d).