Amelia works at a coffee shop on weekends. Every now and then, a customer will order a hot tea and ask Amelia to surprise them with the flavor. The teas are categorized by flavor and caffeine level.Mint Fruity ChaiCaffeine-free 3 5 7Caffeinated 8 4 4What is the probability that a randomly selected tea is fruity or is not caffeine-free?Simplify any fractions.Submit
Question
Amelia works at a coffee shop on weekends. Every now and then, a customer will order a hot tea and ask Amelia to surprise them with the flavor. The teas are categorized by flavor and caffeine level.Mint Fruity ChaiCaffeine-free 3 5 7Caffeinated 8 4 4What is the probability that a randomly selected tea is fruity or is not caffeine-free?Simplify any fractions.Submit
Solution
To solve this problem, we first need to understand the total number of tea options and the number of teas that are either fruity or not caffeine-free.
From the table, we can see that there are 3 + 5 + 7 + 8 + 4 + 4 = 31 total teas.
Next, we need to find the number of teas that are either fruity or not caffeine-free.
The number of fruity teas is 5 + 4 = 9.
The number of teas that are not caffeine-free (i.e., caffeinated) is 8 + 4 + 4 = 16.
However, we can't simply add these two numbers together, because we would be double-counting the fruity, caffeinated teas. So, we need to subtract the number of fruity, caffeinated teas from our total. There are 4 fruity, caffeinated teas.
So, the total number of teas that are either fruity or not caffeine-free is 9 + 16 - 4 = 21.
Finally, we can calculate the probability by dividing the number of desired outcomes (fruity or not caffeine-free teas) by the total
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