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21 Mar 2022, 03:15
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D
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Difficulty:
95%
(hard)
Question Stats:
42% (02:29) correct
58%
(02:43)
wrong
based on 106
sessions
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A certain company sells jellybeans in the following six flavors only: b, c, g, l, p, s. If the jellybeans are sorted randomly into boxes containing exactly 2, 3, 4 different flavors only, what is the probability that any given box contain g jellybeans?
A. 1/6
B. 1/3
C. 2/5
D. 1/2
E. 3/4
Are You Up For the Challenge: 700 Level Questions
A. 1/6
B. 1/3
C. 2/5
D. 1/2
E. 3/4
Are You Up For the Challenge: 700 Level Questions
21 Mar 2022, 18:17
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Bunuel
Breaking Down the Info:
The jellybeans with 2 different flavors have a \(\frac{2}{6} = \frac{1}{3}\) chance of containing g jellybeans.
The jellybeans with 3 different flavors have a \(\frac{3}{6} = \frac{1}{2}\) chance of containing g jellybeans.
The jellybeans with 4 different flavors have a \(\frac{4}{6} = \frac{2}{3}\) chance of containing g jellybeans.
The problem right now is we don't know the distribution of 2/3/4 flavor boxes, but assuming it is equal chance for any of these boxes, then the overall probability for g jellybeans is simply \(\frac{1}{3}*(\frac{1}{3}+\frac{1}{2}+\frac{2}{3}) = \frac{1}{2}\).
Answer: D
26 Aug 2023, 14:55
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