Use for #4 - 9 : A recent poll by the American Automobile Club found that 82.3%

Question

Use for #4 - 9 :

A recent poll by the American Automobile Club found that 82.3% of those surveyed are worried about aggressive drivers on the road. If three people are selected at random, what is the probability that   (Show how you get these either by formula or calculator) –

4.) all will be worried about aggressive drivers on the road?

5.) none will be worried about aggressive drivers on the road?

6.) at least one will be worried about aggressive drivers on the road?

7.) one will be worried about aggressive drivers on the road?

8.) two will be worried about aggressive drivers on the road?

9.) at most two will be worried about aggressive drivers on the road?

Please show all work thank you

Explanation / Answer

Let X be the number of people who are worried This is a binomial distribution problem, with n = 3, p = 0.823

4) P(X = 3) = nCr*pr*(1-p)n-r = 3C3*0.8233*0.1770 = 0.5574

5) P(X = 0) = nCr*pr*(1-p)n-r = 3C0*0.8230*0.1773 = 0.0055

6) P(X >= 1) = P(X=1 + P(X = 2) + P(X = 3) = 3C1*0.8231*0.1772 + 3C2*0.8232*0.1771 + 3C3*0.8233*0.1770
= 0.9945

7) P(X = 1) = 3C1*0.8231*0.1772 = 0.0774

8) P(X = 2) = 3C2*0.8232*0.1771 = 0.3597

9) P(X <= 2) = P(X = 0) + P(X = 1) + P(X = 2) = 3C0*0.8230*0.1773 + 3C1*0.8231*0.1772 + 3C2*0.8232*0.1771
= 0.4426

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