Question

hong 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 9 small balloons, 1 medium balloon, 1 large balloon, and 1 extra - large balloon. he hits one of the balloons at random and wins a stuffed animal of that size.
(a) find the odds against hong winning a small stuffed animal.
(b) find the odds in favor of hong winning a small stuffed animal.

Explanation:

Part (a)

Step1: Determine unfavorable and favorable outcomes

Total balloons = 12. Small (favorable) = 9. Unfavorable (non - small) = 12 - 9 = 3.

Step2: Calculate odds against

Odds against = unfavorable : favorable = 3 : 9 = 1 : 3 (simplified by dividing both by 3).

Step1: Determine favorable and unfavorable outcomes

Favorable (small) = 9. Unfavorable (non - small) = 3.

Step2: Calculate odds in favor

Odds in favor = favorable : unfavorable = 9 : 3 = 3 : 1 (simplified by dividing both by 3).

Answer:

1 to 3

Part (b)