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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. $\newline$ 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 $0.1$ . $\newline$ What is the probability that a randomly chosen tea is fruity or caffeine-free? $\newline$ Write your answer as a whole number, decimal, or simplified fraction.

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Find probabilities using the addition rule

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Q. 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.

\newline

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

.

\newline

What is the probability that a randomly chosen tea is fruity or caffeine-free?

\newline

Write your answer as a whole number, decimal, or simplified fraction.

Denote Events: Let's denote the events as follows: $\newline$ F: The tea is fruity. $\newline$ C: The tea is caffeine-free. $\newline$ We are given the following probabilities: $\newline$ $P(F) = 0.2$ $\newline$ $P(C) = 0.4$ $\newline$ $P(F \text{ and } C) = 0.1$
Use Addition Rule: We need to find the probability that a randomly chosen tea is fruity or caffeine-free. We can use the Addition Rule of Probability: $\newline$ $P(F \text{ or } C) = P(F) + P(C) - P(F \text{ and } C)$
Substitute Values: Substitute the given values into the formula: $\newline$ $P(F \text{ or } C) = 0.2 + 0.4 - 0.1$
Perform Calculation: Now, let's do the calculation: $\newline$ $P(F \text{ or } C) = 0.5$

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