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 3Answera.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 3Answera.6/90b.48/90c.21/90
Solution
The probability of selecting two cookies of the same flavor can be calculated as follows:
First, we calculate the probability of selecting two chocolate cookies: The probability of selecting the first chocolate cookie is 3/10. After eating one chocolate cookie, there are 2 chocolate cookies left out of a total of 9 cookies. So, the probability of selecting a second chocolate cookie is 2/9. Therefore, the probability of selecting two chocolate cookies is (3/10) * (2/9) = 6/90.
Next, we calculate the probability of selecting two butter cookies: The probability of selecting the first butter cookie is 7/10. After eating one butter cookie, there are 6 butter cookies left out of a total of 9 cookies. So, the probability of selecting a second butter cookie is 6/9. Therefore, the probability of selecting two butter cookies is (7/10) * (6/9) = 42/90.
Finally, we add these two probabilities together to find the probability of selecting two cookies of the same flavor: P(S) = P(two chocolate cookies) + P(two butter cookies) = 6/90 + 42/90 = 48/90.
So, the correct answer is b. 48/90.
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