Final answer:
To find the probabilities of a smoothie containing either lemon or mango, we can add the individual probabilities of each event.
Step-by-step explanation:
To find the probability that a smoothie contains lemon or mango, we can add the individual probabilities of each event. The probability of a smoothie containing lemon is 11/20, and the probability of a smoothie containing mango is 9/20.
Adding these probabilities gives us a) P(contains lemon) + P(contains mango) = 11/20 + 9/20 = 20/20 = 1.
To find the probability that a smoothie contains lemon or mango, we can use the formula P(A or B) = P(A) + P(B) - P(A and B). In this case, the probability of a smoothie containing lemon and mango is 3/20.
Substituting the given probabilities, we have b) P(contains lemon or mango) = P(contains lemon) + P(contains mango) - P(contains lemon and mango) = 11/20 + 9/20 - 3/20 = 17/20.
Since the probability of choosing a smoothie containing lemon and the probability of choosing a smoothie containing mango are not mutually exclusive events (since P(contains lemon and mango) is not 0), choosing a smoothie containing lemon and choosing a smoothie containing mango are not mutually exclusive events.