ernest works at a coffee shop on weekends. every now and then, a customer will order a hot tea and ask…
ernest works at a coffee shop on weekends. every now and then, a customer will order a hot tea and ask ernest to surprise them with the flavor. the teas are categorized by flavor and caffeine level. what is the probability that a randomly selected tea is mint given that the tea is caffeine - free? simplify any fractions.
Answer
Explanation:
Step1: Find total caffeine - free teas
Add up the numbers in the "Caffeine - free" column: $6 + 6+4=16$.
Step2: Find number of mint and caffeine - free teas
The number of mint and caffeine - free teas is 6.
Step3: Calculate the conditional probability
The formula for conditional probability $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In the case of frequency tables, if $A$ is the event that the tea is mint and $B$ is the event that the tea is caffeine - free, the probability is $\frac{\text{Number of mint and caffeine - free teas}}{\text{Total number of caffeine - free teas}}=\frac{6}{16}=\frac{3}{8}$.
Answer:
$\frac{3}{8}$