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.)

Question

asked Dec 26, 2020 179k views

1 Answer

Joscelyn · Answer 1 · 2021-01-01T23:39:50+0000

Answer:

(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.