Question 1028846: A certain furniture store found that 20% of the people who enter buy something. Three potential customers walk in. Y means a sale, and N means no sale.
1. The most likely outcome is?
A) YYY B)NNN C)YNY D) NNY E) YNN
I was thinking it might either be NNN or NNY because the percent is so low. Am I right?
2. The probability of NNY is?
A) .128 B) .6 C) .2 D) .5
How would you solve this?
Thanks in advance!
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
The probability of  successes in  trials where  is the probability of success on any given trial is given by:
\ =\ {{n}\choose{k}}\left(p\right)^k\left(1\,-\,p\right)^{n\,-\,k})
Where  is the number of combinations of things taken at a time and is calculated by !})
So the probability of 3 Yes results would be:
\ =\ {{3}\choose{3}}\left(0.2\right)^3\left(0.8\right)^{0}\ =\ 1\ *\ 0.008\ *\ 1\ =\ 0.008)
The probability of 2 Yes results (which could be YYN, YNY, or NYY), would be:
\ =\ {{3}\choose{2}}\left(0.2\right)^2\left(0.8\right)^{1}\ =\ 3\ *\ 0.04\ *\ 0.8\ =\ 0.096)
Each of YYN, YNY, or NYY would be 1/3 of the above result.
The probability of 1 Yes result (YNN, NYN, or NNY) would be:
\ =\ {{3}\choose{1}}\left(0.2\right)^1\left(0.8\right)^{2}\ =\ 3\ *\ 0.2\ *\ 0.64\ =\ 0.384)
Each of YNN, NYN, and NNY would be 1/3 of the above, so P(NNY) = 0.128
The probability of Zero Yes results, NNN, would be:
\ =\ {{3}\choose{0}}\left(0.2\right)^0\left(0.8\right)^{3}\ =\ 1\ *\ 1\ *\ 0.8\ =\ 0.512)
John
My calculator said it, I believe it, that settles it
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