A recent poll by the American Automobile Club found that 73.6% of those surveyed

Question

A recent poll by the American Automobile Club found that 73.6% 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) – Check out my notes for chapter 4 – last page

None will be worried about aggressive drivers on the road?

All will be worried about aggressive drivers on the road?   

At least one will be worried about aggressive drivers on the road?

One will be worried about aggressive drivers on the road?

Two will be worried about aggressive drivers on the road?

At most two will be worried about aggressive drivers on the road?

I need all parts of this to be answered. I have answers but not sure if they are correct. Thanks you

Explanation / Answer

This is an example of a binomial distribution problem.

Probability of success = worry of people = p = 0.736

Probability that people wouldn't worry = 1 - p = 1 - 0.736 = 0.264

Thus,

The probability that:

None will be worried about aggressive drivers on the road?

= (0.264)3

= 0.01839

All will be worried about aggressive drivers on the road?   

= (0.736)3

= 0.39868

At least one will be worried about aggressive drivers on the road?

= 1 - P ( None will be worried)

= 1 - 0.01839

= 0.98161

One will be worried about aggressive drivers on the road?

= 3C1 (0.736) (0.264)2

= 0.15388

Two will be worried about aggressive drivers on the road?

= 3C2 (0.736)2 (0.264)

= 0.4290

At most two will be worried about aggressive drivers on the road?

= 1 - P ( all three are worried)

= 1 - 0.39868

= 0.60132

hope this helps.

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