Question

tony is playing a carnival game. he is blindfolded while he 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 3 small balloons, 5 medium balloons, 2 large balloons, and 2 extra - large balloons. he hits one of the balloons at random and wins a stuffed animal of that size. (a) find the odds in favor of tony winning a medium stuffed animal. (b) find the odds against tony winning a medium stuffed animal.

Explanation:

Step1: Define odds formula

Odds in - favor = $\frac{\text{Number of favorable outcomes}}{\text{Number of unfavorable outcomes}}$, Odds against = $\frac{\text{Number of unfavorable outcomes}}{\text{Number of favorable outcomes}}$

Step2: Identify number of favorable and unfavorable outcomes for winning medium

Total number of balloons = 12. Number of medium balloons (favorable for winning medium) = 5. Number of non - medium balloons (unfavorable for winning medium)=12 - 5=7.

Step3: Calculate odds in favor

Odds in favor of winning a medium stuffed animal = $\frac{5}{7}$, or 5:7.

Step4: Calculate odds against

Odds against winning a medium stuffed animal = $\frac{7}{5}$, or 7:5.

Answer:

(a) 5:7
(b) 7:5