Question

							0 PART A Of 200 students sampeled in KPU courtyard, 100 say they are taking a math course (M), 65 say they are taking a statistics course (S) and 34 are taking both. a. Determine P(M U S): b. Explain the event shown in part a in words. c. What is the probability that a student in this sample has not taken either course? d. Are events M and S mutually exclusive? Provide evidence for your answer using the information given in the problem.        e. If a student has taken the math course, what is the probability that she has also taken the statistics course? If, in order to answer any of the questions below, you need to find other probabilities, please show them as well. f. Are events M and S independent? Provide evidence for your answer using the information given in the problem. Please also explain what your answer means.     PART B John rolls two dice at the same time. He defines the random variable X = sum of the numbers showing. For example, X can have a value of 3 in two ways: First die rolls a 1 and second die rolls a 2, or first one rolls a 2 and second one rolls a 1. Answer the questions below, indicating in the answer cells how you determined the answer (i.e., don't just type in the correct answer, but use cell references and formulas to show your work): a. What are the possible values for X? b. Construct a table showing the probability distribution for x. Sum of dice rolls (X) Probability P(X) c. What is the probability that sum of dice rolls is 4? d. What is the probability that sum of dice rolls is more than 5? e. What is the probability that sum of dice rolls is less than 3? f. What is the probability that sum of dice rolls will be no more than 5 d? g. What is the probability that sum of dice rolls will be more than 11? h. What is the expected value of sum of two dice rolls? i. What is the standard deviation of this probability distribution? j. Write an explanation of what the answers in parts h and I mean. (Make sure that you are not just repeating what the values are but you are explaining the values.) k. Expalin what type of probability is used in this discrete probability distribution.
Instructor mark out of 10:				0
PART A
Of 200 students sampeled in KPU courtyard, 100 say they are taking a math course (M), 65 say they are taking a statistics course (S) and 34 are taking both.
a. Determine P(M U S):
b. Explain the event shown in part a in words.
c. What is the probability that a student in this sample has not taken either course?
d. Are events M and S mutually exclusive? Provide evidence for your answer using the information given in the problem.
e. If a student has taken the math course, what is the probability that she has also taken the statistics course? If, in order to answer any of the questions below, you need to find other probabilities, please show them as well.
f. Are events M and S independent? Provide evidence for your answer using the information given in the problem. Please also explain what your answer means.
PART B
John rolls two dice at the same time. He defines the random variable X = sum of the numbers showing. For example, X can have a value of 3 in two ways: First die rolls a 1 and second die rolls a 2, or first one rolls a 2 and second one rolls a 1. Answer the questions below, indicating in the answer cells how you determined the answer (i.e., don't just type in the correct answer, but use cell references and formulas to show your work):
a. What are the possible values for X?
b. Construct a table showing the probability distribution for x.
	Sum of dice rolls (X)
	Probability P(X)
c. What is the probability that sum of dice rolls is 4?
d. What is the probability that sum of dice rolls is more than 5?
e. What is the probability that sum of dice rolls is less than 3?
f. What is the probability that sum of dice rolls will be no more than 5 d?
g. What is the probability that sum of dice rolls will be more than 11?
h. What is the expected value of sum of two dice rolls?
i. What is the standard deviation of this probability distribution?
j. Write an explanation of what the answers in parts h and I mean. (Make sure that you are not just repeating what the values are but you are explaining the values.)
k. Expalin what type of probability is used in this discrete probability distribution.

Answer 1

Solution

Preparatory Work

Given

Total N – 200 ……………………………………………………………………….(1)

Math M - 100 ……………………………………………………………………….(2)

Stat S - 65 …..……………………………………………………………………….(3)

Both (M ? S) – 34 …………………………………………………………………..(4)

Either (M ? S) = M + S - (M ? S) = 131 …………………………………………..(5)

Neither (M^C ? S^C) = N - (M ? S) = 69 …………………………………………..(6)

Back-up Theory

A or B = A ? B = A + B - A ? B …………………………………..(7)

Neither A nor B = (A^C ? B^C) = N – (A ? B), where N = Total …….(8)

Probability of an event E, denoted by P(E) = n/N …………………………(9)

where n = n(E) = Number of outcomes/cases/possibilities favourable to the event E and N = n(S) = Total number all possible outcomes/cases/possibilities.

If A and B are mutually exclusive, P(A ? B) = 0 ……………………………….(10)

Now, to work out the answer,

Part (a)

P(M U S) = n(M U S)/N [vide (9)]

= 131/200 [vide (5) and (1)]

= 0.655 ANSWER

Part (b)

Event in Part (a) represents the the number of students taking at least one of Math and Stat.

Part (c)

Probability that a student in this sample has not taken either course

= P(M^C ? S^C)

= n(M^C ? S^C)/N [vide (9)]

= 69/200 [vide (6) and (1)]

= 0.345 ANSWER

Part (d)

[vide (4), (9) and (1)]

P(M ? S) = 34/200 = 0.17 ? 0.

So, Vide (10), M and S are not mutually exclusive. ANSWER