Homework answers / question archive / 1) Given U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8}, B = {1, 3, 4, 5, 7} C = {7, 8} a

1) Given U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8}, B = {1, 3, 4, 5, 7} C = {7, 8} a

Math

Share With

---

1) Given U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8}, B = {1, 3, 4, 5, 7} C = {7, 8}

a. A ∩ B ____________________          b. B′ _____________________

c. A′ ∪ B′ ____________________        d. A – B _____________________

e. (A ∩ C) ∩ (A ∪ B) _______________

1. Illustrate each of the following by shading the Venn diagrams below.

a) (T U M)’                                                                                                          b) (T U I U M)

 

                        

 

2. The letters that form the word MISSISSIPPI are placed in a bowl. What are the odds of choosing a “P”?

 

3. You roll a single die numbered from 1 to 6. What is the probability of rolling an odd number, expressed as a fraction?

 

4. A jar contains 12 caramels, 7 mints and 16 dark chocolates. What is the probability of selecting a mint expressed as a fraction?

 

5. A number is chosen at random from a set of whole numbers from 1 to 50. Calculate the probability that the chosen number:

 

a) is not a perfect square


b) is not a multiple of 4


c) is more than 45


d) is not more than 45

6. One hundred people who frequently get migraine headaches were chosen to participate in a study of new anti-headache medicine. Some of the participants were given the medicine; others were not. After one week, the participants were asked if they got a headache during the week. The two-way frequency table summarizes the results. Fill in the missing value and then create a joint and marginal relative frequency table.

 

 

 

 

 

 

 

 

 

 

__________________________________________________________________________________________________

7. 

   Given

 

 

 

 

 

Calculate the joint and marginal frequencies from the table above.

 

1. What is the probability that a participant who did not get a headache took the medicine?

 

2. What is the probability that a participant took medicine given they did not have a headache?

 

 

3. What is the probability that a participant took medicine given they did have a headache?

 

_________________________________________________________________________________________________

8. In a bowl of marbles, there are 10 red ones, 6 green ones, and 8 blue ones.

A___________ If a marble is chosen at random from the bowl, find P(red one or a blue one)?

 

B___________ If two marbles are chosen at random with replacement, find P(red and a blue)?

 

C___________ If two marbles are chosen at random without replacement, find P(they are both red)?

9. A card is chosen from a standard deck of cards. The drawer is looking for clubs and face cards.

 

 

 

 

               

A___________ Find P(Club)

B___________ Find P(Club | Not a Face Card)

C___________ Find P(Club Ç Face Card)

D___________Find P(Not a Club È Not a Face Card)

E___________ Are the events Club and Not a Face Card Independent of each other?

_________________________________________________________________________________________________

10. GIVEN: P(M) = 0.8           P(N) = 0.25          P(R) = 0.6

 

If the probability of P(M and N) = 0.2, are M and N independent? ____________

 

If the probability of P(N and R) = 0.3, are N and R independent? _____________

__________________________________________________________________________________________________

11. Consider that 3 consecutive cards are drawn without replacement from a shuffled deck of cards

A. What is the P(face card and face card)?

 

B. What is the probability that all three cards are hearts?

 

C. What is the probability that all three cards are a King?

 

D. What is the probability that all three cards are the same?

 

 

12. A bag contains 4 blue marbles, 4 red marbles, and 4 green marbles:

 

A. What is the P(green and green) with replacement?

 

 

B. What is the probability of drawing 3 marbles in a row of the same color with replacement?

__________________________________________________________________________________________________