Mr. Turner is about to give one of his students a piece of candy for asking a good question in class. He's going to choose the piece of candy at random out of a bag he brings to class. The following pieces of candy are in the bag: 3 apple gumballs, 6 grape gumballs, and 10 grape suckers. But, there are no apple suckers. What is the probability that the piece of candy Mr. Turner chooses is apple or is a sucker?Do not round intermediate computations, and round your answer to the nearest hundredth.
Question
Mr. Turner is about to give one of his students a piece of candy for asking a good question in class. He's going to choose the piece of candy at random out of a bag he brings to class. The following pieces of candy are in the bag: 3 apple gumballs, 6 grape gumballs, and 10 grape suckers. But, there are no apple suckers. What is the probability that the piece of candy Mr. Turner chooses is apple or is a sucker?Do not round intermediate computations, and round your answer to the nearest hundredth.
Solution
To solve this problem, we first need to determine the total number of candies in the bag. We do this by adding up all the different types of candies:
3 apple gumballs + 6 grape gumballs + 10 grape suckers = 19 total candies
Next, we need to determine the total number of candies that are either apple or a sucker. This includes the apple gumballs and the grape suckers:
3 apple gumballs + 10 grape suckers = 13 candies that are either apple or a sucker
The probability of an event is calculated by dividing the number of ways the event can occur by the total number of outcomes. In this case, the event is choosing a candy that is either apple or a sucker, and the total number of outcomes is the total number of candies in the bag.
So, the probability that the piece of candy Mr. Turner chooses is apple or is a sucker is:
13 (apple or sucker candies) / 19 (total candies) = 0.6842105263157895
Rounding this to the nearest hundredth gives us a probability of 0.68. So, there is a 68% chance that the candy Mr. Turner chooses will be either apple or a sucker.
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