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 $)=$ $\square$

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 $)=$ $\square$

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 it is possible for a member of the drama group to vote for both plays. ‖ ‖ step 2 ⋮ Since each member of the drama group is given only one vote, they can either vote for "Oddems Family," "Thirteenth Night," or not vote at all. ‖ ‖ step 3 ⋮ Therefore, a member cannot vote for both "Oddems Family" and "Thirteenth Night" at the same time, making these events mutually exclusive. ‖ ‖ step 4 ⋮ To find the probability that a randomly selected person voted for either "Oddems Family" OR "Thirteenth Night," we add the probabilities of each event since they are mutually exclusive. ‖ ‖ step 5 ⋮ The probability of voting for "Oddems Family" is $35\%$ and for "Thirteenth Night" is $57\%$. ‖ ‖ step 6 ⋮ Adding these probabilities gives $35\% + 57\% = 92\%$. ‖ ‖ step 7 ⋮ Therefore, the probability that a randomly selected person voted for either play is $92\%$ or $0.92$ in decimal form. ‖ ∻[1] Answer∻ ***A*** ∻[2] Answer∻ $P( ext{Oddems Family OR Thirteenth Night}) = 0.92$ ∻Key Concept∻ ⚹Mutually Exclusive Events⚹ ∻Explanation∻ ⚹Two events are mutually exclusive if they cannot occur at the same time. In this scenario, since each member can only cast one vote, they cannot vote for both plays, making the events mutually exclusive.⚹ ∻Key Concept∻ ⚹Probability of Union of Mutually Exclusive Events⚹ ∻Explanation∻ ⚹The probability of the union of two mutually exclusive events is the sum of their individual probabilities. This is because the occurrence of one event does not affect the occurrence of the other.◊What is the formula to calculate the probability of mutually exclusive events when choosing between "Oddems Family" and "Thirteenth Night"?⍭ Generate me a similar question◊⚹

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