A bag with 10 marbles is shown below. (3 marbles are blue, 1 is yellow, and 6 are red.) A marble is chosen from the bag at random. What are the odds in favor of choosing a blue marble?
Question
A bag with 10 marbles is shown below. (3 marbles are blue, 1 is yellow, and 6 are red.) A marble is chosen from the bag at random. What are the odds in favor of choosing a blue marble?
Solution
The odds in favor of an event are calculated as the ratio of the number of successful outcomes to the number of unsuccessful outcomes.
Step 1: Identify the total number of outcomes. In this case, there are 10 marbles in total.
Step 2: Identify the number of successful outcomes. Here, a successful outcome is drawing a blue marble, and there are 3 blue marbles.
Step 3: Identify the number of unsuccessful outcomes. This is the total number of outcomes minus the number of successful outcomes. So, there are 10 total marbles - 3 blue marbles = 7 marbles that are not blue.
Step 4: Write the odds in favor of the event as the ratio of successful outcomes to unsuccessful outcomes. So, the odds in favor of drawing a blue marble are 3 to 7.
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