Police records in the town of Saratoga show that 12 percent

Police records in the town of Saratoga show that 12 percent of the drivers stopped for speeding have invalid licenses. If 10 drivers are stopped for speeding, find the probabilities.

a.None will have an invalid license.
b. Exactly two will have an invalid license.
c. At least 3 will have invalid licenses

Solution

Police records in the town of Saratoga show that 12 percent of the drivers stopped for speeding have invalid licenses. If 10 drivers are stopped for speeding, find the probabilities.

a.None will have an invalid license.

p=0.12

n=10

P(X=x) = (_nC_x) p^x (1-p)^n-x   

P(X=0) = (₂₀C₀) 0.12⁰ (1-0.12)^10-0  

P(X = 0) = 0.2785

b. Exactly two will have an invalid license.

P(X=2) = (₂₀C₂) 0.12² (1-0.12)^10-2   

P(X = 2) = 0.233

c. At least 3 will have invalid licenses

P(x >=3) = 1-( p(x=0)+p(x=1)+p(x=2)) = 1-(0.2785+0.3798+0.233) =0.1087