Help me plz, I need the solutions of all of them. Thank you very much

Question 6: 1/4Question 7: 3/20Question 8: 13/20Question 9: They are not independent.

Explanation:

1. Build a two-way frequency table filling only the initial information:

                                   Take AMS1303   No take AMS1303   Total

Take FIN1001                         25                                                40

No take FIN1001                    

Total                                       50                                               100

2. Complete the table calculating the missing values by differences:

Take AMS1303 only: 50 - 25 = 25No take AMS1303 and take FIN1001: 40 - 25 = 15No take AMS1303: 100 - 50 = 50No take FIN1001: 100 - 40 = 60No take AMS and no take FIN: 60 - 25 = 35

                                   Take AMS1303   No take AMS1303   Total

Take FIN1001                         25                      15                      40 (F)

No take FIN1001                    25                      35                     60  

Total                                       50                      50                   100 (S)

                                              (M)

3. Question 6: Probability that the chosen student takes only AMS1303

P(M) - P(M∩F) = 50/100 - 25/100 = 25/100 = 1/4

4. Question 7: Probability that the chosen student takes only FIN1001

P(F) - P(M∩F) = 40/100 - 25/100 = 15/100 = 3/20

5. Question 8: Probability that the chosen student takes AMS1303 or FIN1001

P(MUF) = P(M) + P(F) - P(M∩F) = 50/100 + 40/100 - 25/100 = 65/100 = 13/20

6. Question 9: Is the event of selecting a student taking AMS1303 independent of the event of selecting a student taking FIN1001?

We will use contidional probability. Two events are independent only if the probability of one event is equal to the probability is the same as the  probability of the event given that the other event occurs.

Is P(M|F) = P(M) ?

P(M|F) = P(M∩F) / P(F) = (25/100) / (40/100) = 25/40 = 5/8

But P(M) = 50/100 = 1/2

Then, P(M|F) ≠ P(M) , therefore they are not independent

Also, you might determine:

Is P(F|M) = P(F)?

P(F|M) = P(M∩F) / P(M) = (25/100) / (50/100) = 25/50 = 1/2

P(F) = 40/100 = 2/5

Again, of course, P(F|M) ≠ P(F), meaning that they are not independent.

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Step-by-step explanation: