Question

debra is playing a carnival game. she is blindfolded while she throws a dart at a board of 12 balloons, as shown below. each balloon is labeled \s\ for small, \m\ for medium, \l\ for large, or \xl\ for extra - large. the board has 5 small balloons, 1 medium balloon, 4 large balloons, and 2 extra - large balloons. she hits one of the balloons at random and wins a stuffed animal of that size. (a) find the odds against debra winning a medium stuffed animal. (b) find the odds in favor of debra winning a medium stuffed animal.

Explanation:

Step1: Calculate the number of non - medium balloons

The total number of balloons is \(n = 12\). The number of medium balloons is \(m=1\). The number of non - medium balloons is \(12 - 1=11\).

Step2: Find the odds against

The odds against an event \(E\) (winning a medium stuffed animal) is the ratio of the number of unfavorable outcomes to the number of favorable outcomes.
The odds against \(=\frac{\text{Unfavorable}}{\text{Favorable}}=\frac{11}{1}\)

Step3: Find the odds in favor

The odds in favor of an event \(E\) is the ratio of the number of favorable outcomes to the number of unfavorable outcomes.
The odds in favor \(=\frac{\text{Favorable}}{\text{Unfavorable}}=\frac{1}{11}\)

Answer:

(a) \(11:1\)
(b) \(1:11\)