Suppose that we have surveyed a certain population of people, and have determined the following probabilities:
- The probability that a person likes anchovies is .
- The probability that a person likes to read books is .
- The probability that a person likes carpets is .
Suppose we also know that these probabilities are all independent, that is, they do not influence each other at all. Wether a person likes anchovies has nothing to do with whether they like to read or whether they like carpets, and so on. When probabilities are independent, it makes sense to multiply them: for example, the probability that someone likes both anchovies and carpets is the product .
What is the probability that a randomly chosen person likes neither anchovies nor books?
What is the probability that a randomly chosen person likes none of these three things?
Can you generalize? What if we had four, five, or more independent probabilities for things people might like; what would be the probability that a random person didn’t like any of the things?