A recent poll by the American Automobile Club found that 73.6% of those surveyed
ID: 3023253 • Letter: A
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.