Question

The Venn diagram below shows information about the number of smoothie ntaining lemon and mango that are available in a cafe. A smoothie is chos at random. Work out a) P(contains lemon) + P(contains mango) b) P(contains lemon or mango) Give each answer as a fraction in its simplest form. c) Using your answers from parts a) and b), decide whether choosing a smoothie containing lemon and choosing a smoothie containing mango are mutually exclusive events. Write a sentence to explain your answer. Lemon 3 7 11 Mango 9​

Answer 1

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.