A.For questions 1&2, determine

A.For questions 1&2, determine whether each compoundevent described below is mutually inclusive, mutually exclusive,independent, or dependent. Explain your choice.

1. Rolling a 6 on a die and choosing a queen from a deckof cards. (See Ex. 2)

2. A teacher has a prize bag from which she will chooseprizes for two students. The bag contains 8 tootsie rolls and 10lollipops. She will choose for student 1, then for student 2. (SeeEx. 3)

B. Suppose that Adam rolls a fair six-sided die and afair eight-sided die simultaneously. Let A be the event that thesix-sided die is an even number and B be the event that theeight-sided die is an odd number. Using the sample space ofpossible outcomes below, answer each of the followingquestions.

 1 2 3 4 5 6 7 8 1 1,1 1,2 1,3 1,4 1,5 1,6 1,7 1,8 2 2,1 2,2 2,3 2,4 2,5 2,6 2,7 2,8 3 3,1 3,2 3,3 3,4 3,5 3,6 3,7 3,8 4 4,1 4,2 4,3 4,4 4,5 4,6 4,7 4,8 5 5,1 5,2 5,3 5,4 5,5 5,6 5,7 5,8 6 6,1 6,2 6,3 6,4 6,5 6,6 6,7 6,8

3. What is P(A), the probability that the six-sided dieis an even number?

4. What is P(B), the probability that the eight-sideddie is an odd number?

5. What is P( A and B), the probability that thesix-sided die is an even number and the eight-sided die is an oddnumber?

6. Are events A and B independent? Why or whynot?

1) Rolling a 6 on a die and choosing a queen from a deck ofcards are both independent events. This is because the probabilityof one of the events occuring does not affect the probability ofthe other event occuring.

2) In this case, the events are dependent because the prize forstudent 2 is dependent on the prize of student 1. The probabilityof student 2 getting a particular prize is affected by the prizewhich student 1 gets.

3) P(A) = Probability that the six sided die gives an evennumber = 24/48 = 0.5

4)P(B) = Probability that the eight sided die is an ofd number =24/48 = 0.5

5) Probability that the six sided die gives an even number andthe eight sided die gives an odd number =

= P(A and B) = 12/48 = 0.25

6) The events A and B are said to be independent, if P(A and B)= P(A) * P(B)

We know that P(A and B) = 0.25.

P(A) * P(B) = 0.5 * 0.5 = 0.25.

As the condition for independence is satisfied, we can concludethat events A and B are independent.

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