Suppose that among people who file a tax return 75 of people

Suppose that among people who file a tax return, 75% of people fill out tax forms correctly, 9% have an error that favors the taxpayer, 6% have an error that favors the government, and 10% have both kinds of errors.

If 20 tax forms are randomly selected for audit, find the probability that:

12 will be filled out correctly, and 5 will contain an error that favors the taxpayer, and 2 will contain an error that favors the government, and 1 will contain an error of both kinds.

Solution

Solution: Here n=20,

P(x=12) = 20!/12!(20-12)!*(0.75)¹²*(1-0.75)^20-12= 0.06089

P(x=5) = 20!/(20-5)!*5!*(0.09)⁵*(1-0.09)^20-5 = 0.022247

P(x=2) = 20!/(20-2)!*2!*(0.06)² *(1-0.06)^20-2 = 0.22457

P(x=1) = 20!/(20-1)!1!*(0.10)¹ *(1-0.10)¹⁹ = 0.27017