Question
A stoplight at the corner of Lincolnway and Duff Avenue is red 20% of the time. For someone who drives through this stoplight 10 times a week, what is the probability that they will stop at least three times?
Answers
MathMate
The experiment consists of 10 bernoulli (either true or false) experiments over one week.
The probability of success p is 0.3 (so failure, q=0.7)
The probability does not change throughout the week.
This is a binomial distribution, where the probability of r success out of n trials is
P(n,r)=C(n,r)*p^r*q^(n-r)
and C(n,r) is combination function given by
C(n,r)=n!/(r!(n-r)!)
Thus
P(10,0)=1*0.3^0*0.7^10=0.028
P(10,1)=10*0.3*0.7^9=0.121
P(10,2)=45*0.3^2*0.7^8=0.233
and probability of stopping at least three times is
1-(P(10,0)+P(10,1)+P(10,2)
=0.617
The probability of success p is 0.3 (so failure, q=0.7)
The probability does not change throughout the week.
This is a binomial distribution, where the probability of r success out of n trials is
P(n,r)=C(n,r)*p^r*q^(n-r)
and C(n,r) is combination function given by
C(n,r)=n!/(r!(n-r)!)
Thus
P(10,0)=1*0.3^0*0.7^10=0.028
P(10,1)=10*0.3*0.7^9=0.121
P(10,2)=45*0.3^2*0.7^8=0.233
and probability of stopping at least three times is
1-(P(10,0)+P(10,1)+P(10,2)
=0.617