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

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

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

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)=(4)/(7)`

The probability of unfavorable event

`P(E')=1-P(E)=1-(4)/(7)=(3)/(7)`

Odds of event E is

`odds=(P(E))/(P(E'))`

`odds=((4)/(7))/((3)/(7))`

`odds=(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=(P(E))/(P(E'))`

`odds=(0.6)/(0.4)`

`odds=(3)/(2)`

Therefore the odds of event E is 3/2.