Question

Find the odds of each of the following events. (a) an event E with Pr(E) = 4/7 (b) an event E with Pr(E) = 0.6 (a) The odds are to (Simplify your answer.)

Answer 1

Answer:

(a) The odds of event E is 4/3.

(b) The odds of event E is 3/2.

Step-by-step explanation:

Formula for probability of an event:

$Probability=\frac{\text{Favorable outcomes}}{\text{Total outcomes}}$

Formula for odds of an event:

$odds=\frac{\text{Favorable outcomes}}{\text{Unfavorable outcomes}}$

(a)

It is given that

$P(E)=\frac{4}{7}$

The probability of unfavorable event

$P(E')=1-P(E)=1-\frac{4}{7}=\frac{3}{7}$

Odds of event E is

$odds=\frac{P(E)}{P(E')}$

$odds=\frac{\frac{4}{7}}{\frac{3}{7}}$

$odds=\frac{4}{3}$

Therefore the odds of event E is 4/3.

(b)

It is given that

$P(E)=0.6$

The probability of unfavorable event

$P(E')=1-P(E)=1-0.6=0.4$

Odds of event E is

$odds=\frac{P(E)}{P(E')}$

$odds=\frac{0.6}{0.4}$

$odds=\frac{3}{2}$

Therefore the odds of event E is 3/2.