Question

Convert between probability and odds.

(a) Determine the probability for the odds of 4 to 1 against E

(b) Determine the odds for and the odds against event H given the probability P(H) = 1/4 .

Answer 1

Convert between probability and odds.

Probability = (favorable number of outcomes) / (total number of outcomes)

unfavorable number of outcomes = total number of outcomes - favorable number of outcomes

Odds in favor of an event E = (favorable number of outcomes) / (unfavorable number of outcomes)

Odds against and event E = (unfavorable number of outcomes) / (favorable number of outcomes)

Solution

(a) Determine the probability for the odds of 4 to 1 against E.

Odds against E = 4/1

So, unfavorable outcomes = 4 and favorable outcomes = 1

Total outcomes = 4 + 1 = 5

Probability of the event = 1 / 5

P(E) = 1/5

(b) Determine the odds for and the odds against event H given the probability P(H) = 1/4

P(H) = 1/4

favorable outcomes = 1 and total outcomes = 4

unfavorable outcomes = 4 - 1 = 3

Odds in favor of an event H = 1/3 or 1 to 3 or 1:3.

Odds against event H = 3/1 = 3 or 3 to 1 or 3:1.