2.7 - Some Examples

A company has bid on two large construction projects. The company president believes that the probability of winning the first contract is 0.6, the probability of winning the second contract is 0.4, and the probability of winning both contracts is 0.2.

1. What is the probability that the company wins at least one contract?
2. What is the probability that the company wins the first contract but not the second contract?
3. What is the probability that the company wins neither contract?
4. What is the probability that the company wins exactly one contract?

If it is known that \(A\subseteq B\), what can be definitively said about \(P(A\cap B)\)?

If 7% of the population smokes cigars, 28% of the population smokes cigarettes, and 5% of the population smokes both, what percentage of the population smokes neither cigars nor cigarettes?