Answer: (4Cx) × (0.25^x) × (0.75^4-x), mean =1, variance = 0.75
Step-by-step explanation:
Total bottle of wine = 12
Number of spoilt wine = 3
p(spoilt wine) = 3/12 = 1/4 = 0.25, q = 1 - 0.25 = 0.75.
n = number of bottles selected randomly = 4.
Since n = 4, then the experiment is of a binomial.
The probability mass function for a binomial distribution is given as
p(x=r) = nCr × p^r × q^n-r
The distribution for x is given below as
P(X=x) = (4Cx) × (0.25^x) × (0.75^4-x)
The mean for a binomial probability distribution is given as
Mean = np = 4×0.25 = 1
Variance = npq = 4×0.25×0.75 = 0.75
