7. Mary goes into the supermarket. The probability that she buys (a) regular coffee is .30, (b) decaffeinated coffee is .40, and (c) that she buys both is .30. What is the probability that she buys regular coffee, decaffeinated coffee, or both?
To find the probability that Mary buys regular coffee, decaffeinated coffee, or both, we need to apply the principle of inclusion-exclusion.
Let's assign the following probabilities:
P(R) = probability of buying regular coffee = 0.30
P(D) = probability of buying decaffeinated coffee = 0.40
The probability of buying both regular and decaffeinated coffee, P(R ∩ D), is given as 0.30.
Now, we can calculate the probability of buying either regular coffee or decaffeinated coffee or both by using the principle of inclusion-exclusion.
P(R ∪ D) = P(R) + P(D) - P(R ∩ D)
Substituting the given probabilities into the equation, we get:
P(R ∪ D) = 0.30 + 0.40 - 0.30
= 0.40
Therefore, the probability that Mary buys regular coffee, decaffeinated coffee, or both is 0.40.