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The only items on a shelf are 8 green bins and 4 orange bins
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03 Aug 2020, 15:00
03 Aug 2020, 15:00
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15% (02:44) wrong based on 45 sessions
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The only items on a shelf are 8 green bins and 4 orange bins. If 3 bins are to be selected from the shelf, one after the other, at random and without replacement, what is the probability that at least one green bin is selected?
Give your answer as a fraction.
Give your answer as a fraction.
Show: ::
\(\frac{54}{55}\)
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Re: The only items on a shelf are 8 green bins and 4 orange bins
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05 Aug 2020, 06:14
05 Aug 2020, 06:14
4
Carcass wrote:
The only items on a shelf are 8 green bins and 4 orange bins. If 3 bins are to be selected from the shelf, one after the other, at random and without replacement, what is the probability that at least one green bin is selected?
Give your answer as a fraction.
Give your answer as a fraction.
Show: ::
\(\frac{54}{55}\)
We want P(select AT LEAST 1 green bin)
When it comes to probability questions involving "at least," it's best to try using the complement.
That is, P(Event A happening) = 1 - P(Event A not happening)
So, here we get: P(getting at least 1 green bin) = 1 - P(not getting at least 1 green bin)
What does it mean to not get at least 1 green bin? It means getting zero green bins.
So, we can write: P(getting at least 1 green bin) = 1 - P(getting zero green bins)
P(getting zero green bins)
P(getting zero green bins) = P(orange bin 1st AND orange bin 2nd AND orange bin 3rd)
= P(orange bin 1st) x P(orange bin 2nd) x P(orange bin 3rd)
= 4/12 x 3/11 x 2/10
= 1/3 x 3/11 x 1/5
= 1/55
So, P(getting at least 1 green bin) = 1 - 1/55 = 54/55
Answer: 54/55
Cheers,
Brent
General Discussion
Re: The only items on a shelf are 8 green bins and 4 orange bins
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Updated on: 05 Aug 2020, 08:46
Updated on: 05 Aug 2020, 08:46
1
8 green Bins
4 Orange Bins
Experiment: Picking 3 bins out of the 12 bins available without replacement
Event A: at least one of the 3 bins picked is green
Event A Complement: no green bin is picked among the 3 bins picked
Number of Outcomes in A Complement: (4 choose 3)
We choose 3 from 4, because we only want to pick 3 bins out of 4 orange bins
Number of outcomes in the sample space= (12 choose 3)
Here we pick 3 bins out of all the 12 bins.
P(A)=1-P(A complement)= 1-(number of outcomes in A complement)/(number of outcomes in the sample space)= 1-(4 choose 3)/(12 choose 3) = 1-4/220= 216/220= 54/55
Final Answer: 54/55
4 Orange Bins
Experiment: Picking 3 bins out of the 12 bins available without replacement
Event A: at least one of the 3 bins picked is green
Event A Complement: no green bin is picked among the 3 bins picked
Number of Outcomes in A Complement: (4 choose 3)
We choose 3 from 4, because we only want to pick 3 bins out of 4 orange bins
Number of outcomes in the sample space= (12 choose 3)
Here we pick 3 bins out of all the 12 bins.
P(A)=1-P(A complement)= 1-(number of outcomes in A complement)/(number of outcomes in the sample space)= 1-(4 choose 3)/(12 choose 3) = 1-4/220= 216/220= 54/55
Final Answer: 54/55
Originally posted by chacinluis on 04 Aug 2020, 04:32.
Last edited by chacinluis on 05 Aug 2020, 08:46, edited 1 time in total.
Last edited by chacinluis on 05 Aug 2020, 08:46, edited 1 time in total.
