Answer: The probability that 25 or more out of 50 high speed chases result in minor or major accidents is 0.097807364 Â or 9.781%.
The rate of accidents at 0.40 is a constant rate, and hence we can use the binomial distribution to calculate the probability.
The formula for computing the probability with the binomial distribution is:
[tex]P(X=x) = _{n}C_{x}*p^{x}*q^{n-x}[/tex]
where
N  is number of trials  = 50
p is probability of of a hit in a single trial. In this case, p = 0.40
q is probability of of a miss in a single trial. Now [tex]q = 1 - p; q = 1 - 0.4 = 0.6[/tex] for this question
x will take on the whole numbers from 25 Â and continue upto 50
The questions asks us to compute the probability that 25 or more chases will result in an accident. Â
We express this as P( X≥ 25) mathematically.
We can also express P( X≥ 25)  as P (x=25) + P(x=26) + ................ + P(50) i.e the sum of all the individual probabilities when x assumes each of the values from 25 upto 50.
That's why x will take on each of the whole numbers from 25 to 50.
We can compute P( X=25) by substituting the values in the formula above.
[tex]P(X=25) = _{50}C_{25}*0.4^{25}*0.6^{50-25}[/tex]
[tex]P(X=25) = \frac{n!}{x!*(n-x)!}*0.4^{25}*0.6^{50-25}[/tex]
[tex]P(X=25) = \frac{50!}{25!*(50-25)!}*0.4^{25}*0.6^{50-25}[/tex]
[tex]P(x=25) = 0.040463604[/tex]
Similarly we need to compute the probabilities for x =26, 27 and so on until x =50. The sum total of all these probabilities the answer.
The workings have been made in excel and are attached to this answer as a picture.
