Examples

    Question 1

    A fair die is tossed 7 times. We say that a toss is a success if a 5 or 6 appears, otherwise it’s a failure. What is the distribution of the random variable. X representing the number of success out of the 7 tosses? What is the probability that there are exactly 3 success? What is the probobility that there are no success?

         n=7  p=1/3

—

   P(x=3)=(7/3).(1/3)^3.(2/3)^4=560/2187

—

   P(x=0)=(2/7)^7=128/2187

Question 2

       Bob is a high school basketball player. He is a 70% free throw shooter. That means his probability of making a free throw is 0.70. What is the probability that Bob makes his first free throw or his fifth shot? 

 

—P.Q^(X-1)=0,7.(0,3)^4=0,00567

Questions 3

      Suppose that the amount of time one spends in a bank exponentially distributed with mean 10 minutes, N=1/10.  What is the probability than 15 minutes in the bank? What is the probability that a costumer will spend more than 15 minutes in the bank given he is still in the bank after 10 minutes?

 P(x>15)=e^(-15N)=e^(-3/2)

 P(x>15| x>10)=P(x>5)=e^(-1/2)=0.604

Question 4

    If electricity power foilures occur according to a Poisson distribution with an average of 3 failures every twenty weeks, calculate the probability that there will not be more than one failure during a particular week.

      —N:3/20=0,15

    Not more then one failure means we need to include the probabilities for “0 failures” plus “1 failure”

P(x0)+P(x1)=(e^-0,15.0,15)/0! +                   (e^-0,18.0,15)/1! = 0,98981 

 

   

Question 5

   
    We report the dice tossing experiment described. We ask that is the probability that the die will land on a number that is smaller than 4?

—P(x<5)=P(x=1)+P(x=2)+P(X=4)= 1/6+1/6+1/6+1/6=2/3 

 Question 6