TUTORIAL WITH WORK SHOWN FOR THE FOLLOWING QUESTIONS

1. Let S = {b, h, j, n, u, x} be a sample space of an experiment and let E = {b, h} and F = {b, n, x} be events of this experiment.

Are the events E F and E Fc mutually exclusive?

1. Let S = {1, 6, 11, 16, 21, 26}, F = {1, 11, 21}, and G = {21, 26}.

Are the events F and G mutually exclusive?

1. Let S = {5, 10, 15, 20, 25, 30}, F = {5, 15, 25}, and G = {25, 30}.

Are the events F and G complementary?

1. Let S be any sample space and let E and F be any two events associated with the experiment. Describe the event below using the symbols , , and c.

The event that both E and F occur

1. An experiment consists of casting a pair of dice and observing the number that falls uppermost on each die.

(a) Determine the event that the sum of the numbers falling uppermost is less than or equal to 7. (Select all that apply.)

(b) Determine the event that the number falling uppermost on one die is a 4 and the number falling uppermost on the other die is greater than 4. (Select all that apply.)

1. An experiment consists of selecting a letter at random from the letters in the word MASSACHUSETTS and observing the outcomes. (Enter for the empty set.)

(a) What is an appropriate sample space S for this experiment?

(b) Describe the event E "the letter selected is a vowel."

1. An experiment consists of spinning the hand of the numbered disc shown in the following figure and then observing the region in which the pointer stops. (If the needle stops on a line, the result is discounted and the needle is spun again. Enter for the empty set.)

(a) What is the appropriate sample space S for this experiment?

(b) Describe the event E "the spinner points to the number 3."

(c) Describe the event F "the spinner points to an odd number."

1. The manager of a local bank observes how long it takes a customer to complete his transactions at the automatic bank teller machine.

(a) Describe an appropriate sample space for this experiment.

(b) Describe the event that it takes a customer between 2 and 3 min to complete his transactions at the automatic teller machines.