Question

A.For questions 1&2, determine whether each compound event 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 deck of cards. (See Ex. 2)

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

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

	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 die is an even number?

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

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

6. Are events A and B independent? Why or why not?

Answer 1

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

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

3) P(A) = Probability that the six sided die gives an even number = 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 and the 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 conclude that events A and B are independent.

IF YOU FIND THIS ANSWER HELPFUL, PLEASE UP VOTE.