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(a) Show the sample space.

19 / 01 / 2019 Maths

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Question 1: (8 Marks)
M&Ms are blended in a ratio of 13 percent brown, 14 percent yellow, 13 percent red, 24 percent blue, 20 percent orange, and 16 percent green. Suppose you choose a sample of two M&Ms at random from a large bag. 
(a) Show the sample space. 
(b) What is the probability that both are brown?
(c) Both blue? 
(d) Both green?
(e) Find the probability of one brown and one green M&M. 
(f) Actually take 100 samples of two M&Ms (with replacement) and record the frequency of each outcome listed in (b) and (c) above. How close did your empirical results come to your predictions?

Question 2: (6 marks)
A Financial Consultant has classified his clients according to their gender and the composition of their investment portfolio (primarily bonds, primarily stocks, or a balanced mix of bonds and stocks). The proportions of clients falling into the various categories are shown in the following table:

Portfolio Composition
Gender    Bonds    Stocks    Balanced
Male    0.18    0.20    0.25
Female    0.12    0.10    0.15

One client is selected at random, and two events A and B are defined as follows:
A: The client selected is male.
B: The client selected has a balanced portfolio. 

Find the following probabilities:
a) P(A)        (1 mark)
b) P(B)        (1 mark)
c) P(A and B)    (1 mark)
d) P(A or B)        (1 mark)
e) P(A/B)        (1 mark)
f) P(B/A)        (1 mark)

Question 3: (9 Marks)
Find the following probabilities by checking the z table
a) P(-1.52 < Z < 0.7)

b) P((1.15 < Z < 2.45)

c) P(-0.9 < Z < -0.3)

Question 4: (9 marks)
Suppose during weekends, 55 percent of adults go to the beach, 45 percent go to the cinema, and 10 percent go to both the beach and the cinema.
a)    What is the probability that a randomly chosen adult does not go to the cinema?  (3 marks)
b)    What is the probability that a randomly chosen adult go to the beach or the cinema or both?  (3 marks)

c)    What is the probability that a randomly chosen adult doesn`t go to the beach or the cinema? (3 marks)

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