Exercise 38 Page 773

We are given that the odds in favor of Event A are equal to the odds against Event A. Recall that the odds in favor of an event is the ratio between the number of favorable outcomes m and the number of unfavorable outcomes n. Odds in Favor = favorable outcomes/unfavorable outcomes = m/n On the other hand, the odds against an event are equal to the reciprocal of the odds in favor. Odds Against = unfavorable outcomes/favorable outcomes = n/m According to the given information, the odds in favor of Event A are equal to the odds against Event A. Odds in Favor = Odds Against ⇕ m/n = n/m Let's now simplify the obtained equation. Keep in mind that n and m are nonzero positive numbers.

It follows from the given information that m is equal to n. We can now calculate the probability of Event A. The probability is the number of favorable outcomes m divided by the total number of outcomes — the sum of m and n. P(Event A) = m/m + n Since m is equal to n, we can substitute m for n in the expression for the probability.