The theater director offered every member of the drama one vote for which play they preferred to perform. The director found that $35 \%$ voted for The Oddems Family, that $57 \%$ voted for Thirteenth Night, and that $8 \%$ did not vote.

In this group, are the events "Oddems Family" and "Thirteenth Night" mutually exclusive?

Choose 1 answer:
(A) Yes
(B) No

Find the probability that a randomly selected person from this group voted for Oddems Family OR Thirteenth Night.
$P($ Oddems Family OR Thirteenth Night $)=$

Question

The theater director offered every member of the drama one vote for which play they preferred to perform. The director found that $35 \%$ voted for The Oddems Family, that $57 \%$ voted for Thirteenth Night, and that $8 \%$ did not vote.

In this group, are the events "Oddems Family" and "Thirteenth Night" mutually exclusive?

Choose 1 answer:
(A) Yes
(B) No

Find the probability that a randomly selected person from this group voted for Oddems Family OR Thirteenth Night.
$P($ Oddems Family OR Thirteenth Night $)=$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To determine if the events "Oddems Family" and "Thirteenth Night" are mutually exclusive, we need to check if the sum of their probabilities exceeds 100%. ‖ ‖ step 2 ⋮ The probability of voting for "Oddems Family" is 35%, and for "Thirteenth Night" is 57%. ‖ ‖ step 3 ⋮ Adding the probabilities: $35\% + 57\% = 92\%$. ‖ ‖ step 4 ⋮ Since the sum of the probabilities is less than 100% and there is a percentage of people who did not vote, the events can be considered mutually exclusive. ‖ ‖ step 5 ⋮ To find the probability that a person voted for either "Oddems Family" OR "Thirteenth Night", we add the probabilities of the two events. ‖ ‖ step 6 ⋮ Calculating the probability: $P( ext{Oddems Family OR Thirteenth Night}) = 35\% + 57\% = 92\%$. ‖ ∻1 Answer∻ ⚹ (A) Yes, the events are mutually exclusive. ⚹ ⚹ $P( ext{Oddems Family OR Thirteenth Night}) = 92\%$. ⚹ ∻Key Concept∻ ⚹Mutual Exclusivity and Addition Rule in Probability⚹ ∻Explanation∻ ⚹Events are mutually exclusive if they cannot occur at the same time. The addition rule states that the probability of either event occurring is the sum of their individual probabilities, provided the events are mutually exclusive.⚹◊What is the formula for calculating the probability of two events being mutually exclusive?⍭ Generate me a similar question◊

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