You and your friend decide to get your cars inspected. you are informed that 71% of cars pass inspection. if the event of your car's passing is independent of your friend's car, a) what is the probability that your car passes inspection? b) what is the probability that your car doesn't pass inspection? c) what is the probability that both of the cars pass? d) what is the probability that at least one of the two cars passes?

a) 0.71

b) 0.29

c) 0.50

d) 0.91

Step-by-step explanation:

To get the probability that your car pass inspection we use the given information,  if we are informed that 71% of cars pass inspection, that means that from 100 cars ,  71 pass the inspection.  

P=# of possibilities that meet the condition / #of equally likely possibilities.

a) So, the  probability that your car passes inspection is

P(passing) =71/100=0.71

b) We have two options,  passing or not passing the inspection and the Complement Rule states that the sum of the probabilities of an event and its complement must equal 1.

So,  the probability of not passing is

P(not passing)= 1- P(passing)

P(not passing)= 1- 0.71=0.29

c) When we need to know the probability of 2 event happening at the same time,  we multiply both probabilities.

The probability that both of the cars pass= the probability of passing our car*  the probability of passing the car of your friend

P(both passing) =0.71*0.71=0.50

d) The probability that at least one of the two cars passes is

P=1 - (P(not passing))^2=0.91

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