Final answer:
The probability that a customer purchases exactly one of the items, either a novel or a nonfiction book, in a bookstore is 0.6.
Step-by-step explanation:
To find the probability that a customer purchases exactly one item from specific categories in a bookstore, we can use the given probabilities. The probability of buying a novel is 0.6, the probability of buying a nonfiction book is 0.4, and the probability of buying both is 0.2. To find the probability of buying exactly one of the items, we can use the following formula for the probability of either event minus both:
- P(Novel only) = P(Novel) - P(Both).
- P(Nonfiction only) = P(Nonfiction) - P(Both).
The calculations are:
- P(Novel only) = 0.6 - 0.2 = 0.4.
- P(Nonfiction only) = 0.4 - 0.2 = 0.2.
Finally, we add these probabilities to find the probability of purchasing exactly one item:
- P(Exactly one item) = P(Novel only) + P(Nonfiction only) = 0.4 + 0.2 = 0.6.