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02 Mar 2022, 04:09
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
68% (02:03) correct
32%
(02:05)
wrong
based on 515
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Chef Gundy is creating a new dessert that will be made from 3 ingredients. If he has 8 cookies and one flavor of sorbet to choose from, what fraction of the possible arrangements will contain the sorbet?
(A) 1/84
(B) 1/56
(C) 1/9
(D) 1/3
(E) 2/3
(A) 1/84
(B) 1/56
(C) 1/9
(D) 1/3
(E) 2/3
12 Mar 2022, 17:45
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Another way to do this is to just review the probability of NOT having a sorbet for each of the three ingredient slots.
So, Slot 1 probability of NOT having a sorbet is 8/9.
Slot 2 probability is 7/8.
Slot 3 probability is 6/7.
When you multiply these three probabilities, the 8s cancel and 7s cancel, so you are left with 6/9 = 2/3.
If there is a 2/3 probability of NOT having a sorbet, then the remaining 1/3 must be the probability that the recipe WILL include the sorbet.
With this method you are going to complete the problem in less than 60 seconds.
So, Slot 1 probability of NOT having a sorbet is 8/9.
Slot 2 probability is 7/8.
Slot 3 probability is 6/7.
When you multiply these three probabilities, the 8s cancel and 7s cancel, so you are left with 6/9 = 2/3.
If there is a 2/3 probability of NOT having a sorbet, then the remaining 1/3 must be the probability that the recipe WILL include the sorbet.
With this method you are going to complete the problem in less than 60 seconds.
General Discussion
07 Mar 2022, 01:32
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Total desserts which can be made with 3 ingredients: \(\frac{9!}{3!6!} = 84\)
Total desserts which contain 2 cookies and sorbet: \(\frac{8!}{2!6!}= 28 \)
Fraction of the possible arrangements will contain sorbet: \(\frac{28}{84}\)
\(\frac{1}{3}\)
Answer D
Total desserts which contain 2 cookies and sorbet: \(\frac{8!}{2!6!}= 28 \)
Fraction of the possible arrangements will contain sorbet: \(\frac{28}{84}\)
\(\frac{1}{3}\)
Answer D
