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Answer:
The probability that exactly 12 buyers would prefer green
=0.00555
Step-by-step explanation:
We are given that
p=50%=50/100=0.50
n=14
We have to find the probability that exactly 12 buyers would prefer green.
q=1-p
q=1-0.50=0.50
Using binomial distribution formula
[tex]P(X=x)=nC_r p^r q^{n-r}[/tex]
[tex]P(x=12)=14C_{12}(0.50)^{12}(0.50)^{14-12}[/tex]
[tex]P(x=12)=14C_{12}(0.50)^{12}(0.50)^2[/tex]
[tex]P(x=12)=14C_{12}(0.50)^{14}[/tex]
[tex]P(x=12)=\frac{14!}{12!2!}(0.50)^{14}[/tex]
[tex]P(x=12)=\frac{14\times 13\times 12!}{12!2\times 1}(0.50)^{14}[/tex]
[tex]P(x=12)=91\cdot (0.50)^{14}[/tex]
[tex]P(x=12)=0.00555[/tex]
Hence, the probability that exactly 12 buyers would prefer green
=0.00555