Statistics Probability Question

Question

Nine percent of vehicles have an expired inspection sticker, three percent have an expired registration and two percent have both. What is the probability a randomly selected vehicle has a valid inspection sticker and a valid registration?

Answer 1

let the number of vehicles be 100

then number of vehicles  with both expired =2 

number of vehicles with expired registration but not expired sticker is 1 

 

and no. of vehicles with exp sticker but not exp registration is 7.

 

so out of 100 ,no of vehicles having atleast one of these is 2+1+7=10 

hence number of vehicles having none of the above is 90 

 

hence required probability is 90/100 ie 9/10