Question

Question 3: You are going to roll a 6-sided dice a total of ? times. Let’s define the following events: Event I: appearance of number 4 Event II: appearance of odd number What is the probability that the first occurrence of Event I occurs before the first occurrence of Event II? Hint: you can use simulation to solve this problem.

Question 4: An inspection system has a 95% probability of correctly classifying a defective part as defective, and a 3% probability of incorrectly classifying a good part as defective. This system is going to be used to inspect a batch of parts, which consists of 2% actually defective parts. What is the probability that an item classified as defective is truly defective?

Answer 1

3)

probability of event I =P(Event 1) =1/6

probability of event II =P(Event II) =3/6 =1/2 (since there are 3 odd numbers )

also as Event I and Event II are mutually exclusive, therefore

probability that the first occurrence of Event I occurs before the first occurrence of Event II

=P(Event 1)/(P(Event 1)+P(Event 2)) =(1/6)/((1/2)+(1/6)) =0.25

4)

P(tested defective)=P(defective and tested defective)+P(not defective and tested defective)
	=0.02*0.95+0.98*0.03=0.0484

Therefore P(defective|tested defective)=0.02*0.95/0.0484=0.3926