Please show work not just final answers Thanks 116 A box of

Please show work not just final answers!! Thanks.

116. A box of cookies contains three chocolate and seven butter cookies. Miguel randomly selects a cookie and eats it. Then he randomly selects another cookie and eats it. (How many cookies did he take?) a. Draw the tree that represents the possibilities for the cookie selections. Write the probabilities along each branch of the tree. b. Are the probabilities for the flavor of the SECOND cookie that Miguel selects independent of his first selection? Explain. c. For each complete path through the tree, write the event it represents and find the probabilities. d. Let S be the event that both cookies selected were the same flavor. Find P(S). e. Let T be the event that the cookies selected were different flavors. Find P(T) by two different methods: by using the complement rule and by using the branches of the tree. Your answers should be the same with both methods. f. Let U be the event that the second cookie selected is a butter cookie. Find P(U).

Solution

No. The probability differs according to the first selection, as no of chocolate or butter changes.

c) P(Both chocolate) = 42/90 = 7/15

   P(I choco and second butter) = 7/30

P(I butter and second choco) = 7/30

P(Both butter) = 1/15

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d) P(S) = P(BOth choco)+P(both butter)

= 8/15

e) P(T) = 1-8/15 = 7/15

or P(T) = P(BUtter and choco)+P(choco and butter)

= 7/30+7/30 = 7/15

f) P(U) = 7/10(3/9) + 3/10(2/9)

=3/10