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?

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JeanaShupp JeanaShupp · Answer 1 · 2019-07-15T10:13:35+02:00

Answer: 0.0325

Step-by-step explanation:

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

[tex]P(X=x)=^nC_x\ p^x\ (1-p)^{n-x}[/tex], 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 : [tex]p= 0.319[/tex]

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

[tex]P(X=3)=^3C_3\ (0.319)^3\ (1-0.319)^{3-3}\\\\=(1) (0.319)^3(1)\\=0.032461759\approx0.0325[/tex]

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