Samir works at a coffee shop on weekends. Every now and then, a customer will order a hot tea and ask Samir to surprise them with the flavor. The teas are categorized by flavor and caffeine level.The probability that a tea is fruity is 0.2, the probability that it is caffeine-free is 0.4, and the probability that it is fruity and caffeine-free is 0.1.What is the probability that a randomly chosen tea is fruity or caffeine-free?Write your answer as a whole number, decimal, or simplified fraction.
Question
Samir works at a coffee shop on weekends. Every now and then, a customer will order a hot tea and ask Samir to surprise them with the flavor. The teas are categorized by flavor and caffeine level.The probability that a tea is fruity is 0.2, the probability that it is caffeine-free is 0.4, and the probability that it is fruity and caffeine-free is 0.1.What is the probability that a randomly chosen tea is fruity or caffeine-free?Write your answer as a whole number, decimal, or simplified fraction.
Solution
The probability that a randomly chosen tea is either fruity or caffeine-free can be found using the formula for the probability of the union of two events: P(A U B) = P(A) + P(B) - P(A ∩ B).
Here, event A is the tea being fruity and event B is the tea being caffeine-free.
P(A) = Probability that the tea is fruity = 0.2 P(B) = Probability that the tea is caffeine-free = 0.4 P(A ∩ B) = Probability that the tea is both fruity and caffeine-free = 0.1
Substituting these values into the formula gives:
P(A U B) = P(A) + P(B) - P(A ∩ B) = 0.2 + 0.4 - 0.1 = 0.5
So, the probability that a randomly chosen tea is either fruity or caffeine-free is 0.5 or 50%.
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