QUESTION 1 (31 MARKS)
In a school sports day, there are 110 students taking part in 3 events i.e. athletic, netball, and soccer. Some of them are also supporters. Overall 43 of them are girls. 40 students take part in athletic. There are 25 girls taking part in netball, and 5 play netball and athletic. As for boys, only 30 boys play soccer, and only 15 take part in athletic. Meanwhile, 20 students act as supporters. The number of boys who play soccer only is 6 times more than girls who take part in netball and athletic. Note that the events only girls play netball and only boys play soccer are mutually exclusive.
a. Illustrate the events. Write the proper symbol for each event.(16 marks)
b. If one student is selected, find the probability of
i. student who play soccer and an athletic. (1 mark)
ii. student who play netball but not an athletic. (1 mark)
iii. student who only take part in athletic. (9 marks)
iv. student who take part in netball given that she is not an athletic, or the student play soccer. (4 marks)
QUESTION 2 (20 MARKS)
Each member of the group toss 4 coins 10 times and observe how many heads are shown. Then combine all observations.
a. Create frequency table displaying the results. (9 marks)
b. Compare the frequency table to the theoretical probability distribution for the outcome when 4 coins are tossed. (5 marks)
c. Find the mean for the frequency table. Compare your answer with the mean for the probability distribution and give the interpretation. (6 marks)
QUESTION 3 (21 MARKS)
Excell Computers promptly shipped two servers to its biggest client. The company profits RM5,000 on each one of these big systems. The shipping worker randomly selected the system without replacement that were delivered from 15 computers in stock.The system contain 4 refurbished computer, with 11 new computers in the warehouse.
If the client gets two new computers, Excell earns RM10,000 profit. If the client gets a refurbished computer, it's coming back for replacement and Excell must pay the RM400 shipping fee, with leaves RM9,600 profit. If both computers shipped are refurbished, consequently the client will return both and cancel the order. As a result, Excell will be out any profit and left with RM8,000 in shipping cost. Let X be a random variable for the amount of the profit earned on the order.
a. Illustrate the event. (6 marks)
b. Construct a probability distribution table and the amount of profit earned for the computer condition. (12 marks)
c. Calculate the expected profit then interpret the value. (3 marks)
QUESTION 4 (28 MARKS)
Refer to the attached file name: "Data.xlsx".
a. Find the conditional probability of STPM given male, and the joint probability of female and matriculation. (9 marks)
b. Find the conditional probability of executive given others, and the marginal probability of lecturer.(8 marks)
c. Determine whether decision science is independent of private, and prove your answer.Check whether these events is mutually exclusive.(11 marks)
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