Question

There is a $\frac{3}{5}$ chance of rain today. What are the odds against it raining today?

• A. $3:5$
• B. $3:2$
• C. $2:3$
• D. $2:5$

Answer 1

The correct option is C $2:3$

$\underset{–}{\text{Given}:}$
Chance of raining today $=\frac{3}{5}$

We know, $\text{P(rain)}=\frac{\text{Favorable number of outcomes}}{\text{Total number of outcomes}}$

$\therefore$ Number of favorable outcomes $=3k$
And number of total outcomes $=5k$

Thus, number of unfavorable outcomes $=$ Total number of outcomes $-$ Number of favorable outcomes

$\Rightarrow$ Number of unfavorable outcomes $=5k-3k=2k$

$\underset{–}{\text{Need to Find}:}$
Odds against it raining today

$\text{Odds against}=\frac{\text{Number of unfavorable outcomes}}{\text{Number of favorable outcomes}}$

$\Rightarrow \text{Odds against}=\frac{2k}{3k}=\frac{2}{3}=2:3$

Therefore, option (c.) is the correct choice.