Answer:
The probability that exactly 10 buyers would prefer green is 0.0025.
Step-by-step explanation:
Let the random variable X be defined as the number of buyers who would prefer green.
The probability of a buyer preferring Green is, P (X) = p = 0.40.
The sample of buyers selected is of size n = 12.
The color preference of the buyers are independent of each other.
The random variable X satisfies all the conditions of a Binomial distribution.
Thus, [tex]X\sim Bin(12, 0.40)[/tex]
The probability function of a Binomial distribution is:
[tex]P (X=x)={n\choose x}p^{x}(1-p)^{n-x};\ x=0,1,2,...[/tex]
Compute the probability that exactly 10 buyers would prefer green as follows:
[tex]P (X=10)={12\choose 10}(0.40)^{10}(1-0.40)^{12-10}\\=66\times 0.0001049\times0.36\\=0.002491\\\approx0.0025[/tex]
Thus, the probability that exactly 10 buyers would prefer green is 0.0025.
