Question

If the odds against picking a red marble is $4:5,$ what is the probability of picking a red marble?

• A. $\frac{4}{5}$
• B. $\frac{4}{9}$
• C. $\frac{5}{9}$
• D. None of the above

Answer 1

The correct option is C $\frac{5}{9}$

$\underset{–}{\text{Given}:}$
Odds against picking a red marble $=4:5$

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

Let the odd against be k
$\therefore$ Number of unfavorable outcomes $=4k$
And number of favorable outcomes $=5k$

Thus, total number of outcomes $=$ Number of unfavorable outcomes $+$ Number of favorable outcomes

$\Rightarrow$ Total number of outcomes $=4k+5k=9k$

$\underset{–}{\text{Need to Find}:}$
Probability of picking a red marble

$\text{P(picking red marble)}=\frac{\text{Favorable number of outcomes}}{\text{Total number of outcomes}}$

$\Rightarrow \text{P(picking red marble)}=\frac{5k}{9k}=\frac{5}{9}$

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