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A store recently released a new line of alarm clocks that emits a smell to wake you up in the morning. The head of sales tracked buyers' ages and which smells they preferred. Bacon Cinnamon 4 3 Under 13 years old A teenager 3 3 What is the probability that a randomly selected buyer is under 13 years old given that the buyer purchased a clock scented like cinnamon? Simplify any fractions.

Respuesta :

Let's call event A buyers under 13 years old, and event B is a clock scented like cinnamon.

First, we find the probability of A and B

[tex]P(A\cap B)=P(A)\cdot P(B)=\frac{7}{13}\cdot\frac{6}{13}=\frac{42}{169}[/tex]

Then, we use the conditional probability formula to find the probability of A given B.

[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}=\frac{\frac{42}{169}}{\frac{6}{13}}=\frac{42\cdot13}{169\cdot6}=\frac{7}{13}[/tex]

Hence, the probability of A given B is 7/13.

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