Suppose that only 30% of all drivers come to a complete stop at an intersection

Question

Suppose that only 30% of all drivers come to a complete stop at an intersection having flashing red lights in all directions when no other cars are visible. Assuming the number of drivers who come to a complete stop is a Binomial random variable, w hat is the probability that, of 20 randomly chosen drivers coming to an intersection under these conditions. At most 6 will come to a complete stop? Exactly 6 will come to a complete stop? At least 6 come to a complete stop? How many of these drivers do you expect to come to a complete stop?

Explanation / Answer

a) Probbaility of success, p=0.30, number of trials, n=20 and specific number of success in n trials is r=6. Substituting values in following formula, P(X,r)=nCr(p)^r(q)^n-r, obtain required probability.

P(X<=6)=P(X=0)+...+P(X=6)=0.608

b) P(X=6)=20C6(0.30)^6(0.70)^14=0.1916

c) P(X>=6)=1-P(X<6)=1-[P(X=0)+...+P(X=5)]=1-0.4164=0.5836

d) Less than 6 drivers will come to completely stop.

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