A spinner with 9 equally sized slices is shown below. (5 slices are red, 2 are blue, and 2 are yellow.) The dial is spun and stops on a slice at random. What are the odds in favor of landing on a red slice?
Question
A spinner with 9 equally sized slices is shown below. (5 slices are red, 2 are blue, and 2 are yellow.) The dial is spun and stops on a slice at random. What are the odds in favor of landing on a red slice?
Solution
The odds in favor of an event are calculated as the ratio of the probability of the event happening to the probability of the event not happening.
Step 1: Calculate the total number of outcomes. In this case, the spinner has 9 slices, so there are 9 possible outcomes.
Step 2: Calculate the number of favorable outcomes. In this case, landing on a red slice is the favorable outcome, and there are 5 red slices. So, there are 5 favorable outcomes.
Step 3: Calculate the number of unfavorable outcomes. This is done by subtracting the number of favorable outcomes from the total number of outcomes. So, 9 total outcomes - 5 favorable outcomes = 4 unfavorable outcomes.
Step 4: Calculate the odds in favor of the event. This is done by forming a ratio of the number of favorable outcomes to the number of unfavorable outcomes. So, the odds in favor of landing on a red slice are 5 to 4.
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