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A certain candy store sells jellybeans in the following six
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01 Aug 2018, 10:30
01 Aug 2018, 10:30
Expert Reply
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Question Stats:
40% (02:13) correct
59% (02:12) wrong based on 110 sessions
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A certain candy store sells jellybeans in the following six flavors only: banana, chocolate, grape, lemon, peach and strawberry. The jellybeans are sorted into boxes containing exactly 2, 3 or 4 different flavors, with each possible assortment of flavors appearing in exactly one box. What is the probability that any given box contains grape jellybeans?
A. 16
B. 13
C. 25
D. 12
E. 34
A. 16
B. 13
C. 25
D. 12
E. 34
Re: A certain candy store sells jellybeans in the following six
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18 Nov 2018, 20:02
18 Nov 2018, 20:02
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AE wrote:
Please provide a short method.
Carcass wrote:
A certain candy store sells jellybeans in the following six flavors only: banana, chocolate, grape, lemon, peach and strawberry. The jellybeans are sorted into boxes containing exactly 2, 3 or 4 different flavors, with each possible assortment of flavors appearing in exactly one box. What is the probability that any given box contains grape jellybeans?
A. 16
B. 13
C. 25
D. 12
E. 34
A. 16
B. 13
C. 25
D. 12
E. 34
Let us choose that none are grape jellybeans..
1) when the box contains 2 flavours -
total ways - T1=6C2=15 and without jelly beans - W1=5C2=10
2) when the box contains 3 flavours -
total ways - T2=6C3=20 and without jelly beans - W2=5C3=10
3) when the box contains 4 flavours -
total ways - T2=6C4=15 and without jelly beans - W2=5C4=5
Probability that jelly is not there = W1+W2+W3T1+T2+T3=10+10+515+20+15=2550=12
so Probability that jelly is there = 1−12=12
D
Re: A certain candy store sells jellybeans in the following six
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03 Aug 2018, 21:10
03 Aug 2018, 21:10
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Carcass wrote:
A certain candy store sells jellybeans in the following six flavors only: banana, chocolate, grape, lemon, peach and strawberry. The jellybeans are sorted into boxes containing exactly 2, 3 or 4 different flavors, with each possible assortment of flavors appearing in exactly one box. What is the probability that any given box contains grape jellybeans?
A. 16
B. 13
C. 25
D. 12
E. 34
A. 16
B. 13
C. 25
D. 12
E. 34
Here,
In this type we find the probability of no grape then 1 - probability of no grape will give the answer
To start with let us take the first option of the box containing 2 flavors:
Therefore the probability of box containing 2 flavors = 13(Since there are 3 box containing 2 flavors, 3 flavors or 4 flavors)
Now probability of no grape in that box = 56∗45=23.
Therefore the probability of having 2 flavors and no grape = 13∗23=29.
the probability of box containing 3 flavors = 13(Since there are 3 box containing 2 flavors, 3 flavors or 4 flavors)
Probability of no grape in the 3 flavor box = 56∗45∗34=12.
Therefore the probability of having 2 flavors and no grape = 13∗12=16.
the probability of box containing 4 flavors = 13(Since there are 3 box containing 2 flavors, 3 flavors or 4 flavors)
Probability of no grape in the 4 flavor box = 56∗45∗34∗23=13.
Therefore the probability of having 4 flavors and no grape = 13∗13=19.
Therefore probability of no grape in 2, 3 or 4 flavor box = 29+16+19=12.
Therefore the probability of having grape in any given box = 1−12=12.
