Final answer:
The probability that a randomly selected buyer is under 13 years old given that the buyer purchased a clock scented like cinnamon is 1/2 or 50%.
Step-by-step explanation:
The question is asking for the probability that a buyer is under 13 years old given that they purchased a clock scented like cinnamon. To find this probability, we will use the table provided:
- Bacon: 4 (Under 13 years old), 3 (Teenagers)
- Cinnamon: 3 (Under 13 years old), 3 (Teenagers)
From the table, we see that there are 3 buyers under 13 years old who preferred the cinnamon scent, and there are a total of 3 (Under 13 years old) + 3 (Teenagers) = 6 buyers who chose the cinnamon scent. We can calculate the conditional probability with the formula P(A|B) = P(A ∩ B) / P(B).
In this case:
- P(A) is the probability that a buyer is under 13 years old.
- P(B) is the probability that a buyer chose the cinnamon scent.
- P(A ∩ B) is the probability that a buyer is under 13 years old and chose the cinnamon scent.
The probability P(A ∩ B) is 3 out of the total number of cinnamon buyers, which is 6, so P(A ∩ B) = 3/6. Now, since P(B) is the scenario that we know a buyer chose the cinnamon scent, P(B) is actually 1 (since it is given that the buyer chose cinnamon). Therefore, the probability that a buyer is under 13 years old given that they purchased a clock scented like cinnamon is P(A|B) = P(A ∩ B) / P(B) = (3/6) / 1 = 1/2 or 50%.