Question

He probability that federal income tax returns will have 0, 1, or 2 errors is 0.73, 0.23, and 0.04, respectively. if 10 randomly selected returns are audited, what is the probability that eight will have no errors, two will have one error, and none will have two errors?

Answer 1

p1 = 0.73
p2 = 0.23
p3 = 0.04

n1 = 8
n2 = 2
n3 = 0
n = n1+n2+n3 = 8+2+0 = 10

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Multinomial Probability:

`\left((n!)/(n_(1)!*n_(2)!*n_(3)!)\right)*\left(p_(1)\right)^{n_(1)}*\left(p_(2)\right)^{n_(2)}*\left(p_(3)\right)^{n_(3)}`


`\left((10!)/(8!*2!*0!)\right)*\left(0.73\right)^(8)*\left(0.23\right)^(2)*\left(0.04\right)^(0)`


`\left(45\right)*\left(0.73\right)^(8)*\left(0.23\right)^(2)*\left(0.04\right)^(0)`


`\left(45\right)*\left(0.0806460091894081\right)*\left(0.0529\right)*\left(1\right)`


`\left(45\right)*\left(0.00426617388611969\right)`


`0.191977824875386`

To three decimal places, the answer is approximately 0.192, which converts to 19.2%