An experiment consists of three fair, different coloured dice being rolled (the dice are 6-sided and the sides show numbers 1, \ldots ,61,…,6). Let AA be the event that none of the dice shows numbers 1 Q3.1 If we denote by SS the sample space of this experiment, what is the size of SS? Q3.2 What is the probability of AA? Q3.3 What is the probability of BB? Q3.4 What is the probability of A\cap BA∩B? Q3.5 Are the events AA and BB independent? (You must justify your answer!)

Suppose that we roll two fair dice, one red and one blue. Then there are 36 possible outcomes in the sample space, as shown in the table below. Blue Die 1 4 6. 1 (1,1) (1,2) (1,3) (1,4) (1,5) (1,6) 2 (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) 3 (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) 84 (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) A 5 (5,1) (5,2) (5,3) (5,4) (5,5) (5,6) 6 (6,1) (6,2) (6,3) (6,4)| (6,5) (6,6) Suppose we write the sample space in terms of the number of dots facing up on the two dice. That is, write S = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. Use the table to answer each of the following: Complete the probability distribution function (pdf). Enter your answer as a fraction. Sample space Probability 2 3 4.

The manager of a local bank observes how long it takes a customer to complete his transactions at the automatic bank teller machine (ATM). 1) Describe an appropriate sample space for this experiment. a. {t | t < 0} b.{t | t > 0} c. {t | t = 0} 2) Describe the event that it takes a customer between 2 and 3 min to complete his transactions at the ATM. a. {t | 2 ≤ t ≤ 3} b. {t | t ≤ 2} c. {t | t > 0} d. {t | t ≤ 3} e. {t | t > 2}

Create Confidence Interval from a Simulation