Question

studies show that excessive speed is a contributor to 70% of accidents. An insurance analyst reviews accidents, paying particular attention to whether excessive speed is a factor.

a) What is the probability that 3 of the next 8 accidents have excessive speed as a factor

b) what is the probability that no more than 10 accidents are reviewed before 6 have excessive speed as a contributing factor

Answer 1

a)

here this is binomial with parameter n=8 and p=0.7

  probability that 3 of the next 8 accidents have excessive speed as a factor:

P(X=3)=(8C3)*(0.7)³*(0.3)⁵ =0.0467

b)

probability that no more than 10 accidents are reviewed before 6 have excessive speed as a contributing factor:

P(at most 5 have excessive speed in first 10):

P(X<=5)=P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)=

∑x=05 (10Cx)0.7x(0.3)(10-x)    =

0.1503