A box of cookies contains three chocolate and seven butter cookies. A person randomly selects a cookie and eats it. Then the person randomly selects another cookie and eats it. Use the tree diagram below to answer the following question.Let S be the event that both cookies selected were the same flavor. Find P(S).Question 5Answera.6/90b.48/90c.21/90
Question
A box of cookies contains three chocolate and seven butter cookies. A person randomly selects a cookie and eats it. Then the person randomly selects another cookie and eats it. Use the tree diagram below to answer the following question.Let S be the event that both cookies selected were the same flavor. Find P(S).Question 5Answera.6/90b.48/90c.21/90
Solution
The event S can occur in two ways: either the person selects two chocolate cookies or two butter cookies.
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The probability of selecting two chocolate cookies is (3/10) * (2/9) = 6/90.
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The probability of selecting two butter cookies is (7/10) * (6/9) = 42/90.
To find the total probability of event S, we add these two probabilities together:
P(S) = 6/90 + 42/90 = 48/90.
So, the correct answer is b. 48/90.
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