Question

Suppose that a poll finds that 31.9​% of taxpayers who filed their tax return electronically​ self-prepared their taxes. If three tax returns submitted electronically are randomly​ selected, what is the probability that all three were​ self-prepared?

Answer 1

Answer: 0.0325

Explanation:

Binomial probability distribution formula for x successes in n trials:-

`P(X=x)=^nC_x\ p^x\ (1-p)^(n-x)`, where n is the number of trials , p is the probability of success.

Given : The probability that taxpayers who filed their tax return are electronically​ self-prepared their taxes :
`p= 0.319`

If three tax returns submitted electronically are randomly​ selected, then the probability that all three were​ self-prepared is given by :-

`P(X=3)=^3C_3\ (0.319)^3\ (1-0.319)^(3-3)\\\\=(1) (0.319)^3(1)\\=0.032461759\approx0.0325`

Hence, the probability that all three were​ self-prepared =0.0325