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Dr. ZABDAWI Sample EXII/Math 2101 7/6/07
1.A bag contains 6 red marbles, 3 blue marbles, and 7 green marbles. If a marble is randomly selected, what is the probability that it is blue?
(a)(b)
(c)(d)
2.A coin is tossed three times. List the elements of the sample space. Note: H represents “heads,” and T represents “tails.”
(a){HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
(b){HTT, THT, HTH, HHH, TTH, TTT}
(c){HHH, HTT, HTH, TTT, HTT, THH, HHT, THT}
(d){HHH, TTT, THT, HTH, HHT, TTH, HTH}
3.In a box of 11 parts, four of the parts are defective. Two parts are selected, one after the other, at random. Find the probability that both parts are defective. (NOTE: The parts are selected without replacement).
(a)(b)
(c)(d)
The table below summarizes the course grades of 80 college students by gender. Use the table to answer Questions 4 through 6.
A / B / C / D / F / TOTALMale / 8 / 14 / 16 / 8 / 4 / 50
Female / 4 / 6 / 12 / 8 / 0 / 30
TOTAL / 12 / 20 / 28 / 16 / 4 / 80
4.If one student is randomly selected, find the probability that the student made a “B”.
(a)(b)
(c)(d)
5.If one student is randomly selected, find the probability that the student is a male and an “A” student.
(a)(b)
(c)(d)
6.If one student is randomly selected, find the probability that the student is a female or a “C” student.
(a)(b)
(c)(d)
7.A tourist in France wants to visit 11 different cities. If the route is randomly selected, what is the probability that she will visit the cities in alphabetical order? Express your answer as a fraction. Assume no two cities start with same letter.
(a)(b)
(c)(d)
8.A class of 30 students is assigned to write an essay. Suppose 4 essays are randomly chosen for awards of $10, $7, $5, and $3. How many different ways can this be done?
(a)120(b)27,405
(c)4(d)657,720
9.A class of 30 students is assigned to write an essay. Suppose 4 essays are randomly chosen to appear on the class bulletin board. How many different ways can this be done?
(a)120(b)27,405
(c)4(d)657,720
10.Determine whether the following is a probability distribution. Explain why or why not.
x / P(x)0 / 0.243
1 / 0.167
2 / 0.213
3 / 0.149
4 / 0.232
5 / 0.164
(a)Yes, it is a probability distribution because the sum of the probabilities is equal to 1 and each individual probability is between 0 and 1, inclusive.
(b)No, it is not a probability distribution because the sum of the probabilities is not equal to 1.
(c)No, it is not a probability distribution because the some of the probabilities is not between 0 and 1, inclusive.
(d)None of the above.
The random variable x is the number of houses sold by a realtor in a single month at the Sendsom’s Real Estate Office. Its probability distribution is given below. Use it to answer Questions 11 and 12.
x / 0 / 1 / 2 / 3 / 4 / 5 / 6 / 7P(x) / 0.24 / 0.01 / 0.12 / 0.16 / 0.01 / 0.14 / 0.11 / 0.21
11.Find the mean of the probability distribution.
(a)3.35 houses(b)3.40 houses
(c)3.50 houses(d)3.60 houses
12.Find the standard deviation of the probability distribution.
(a)2.62 houses(b)6.68 houses
(c)4.45 houses(d)2.25 houses
Use the following scenario to answer Questions 13 through 17.
Assume that a company finds that an average of 30% of all new employees resign in the first year. Suppose the company considers the next 12 employees hired.
13.Find the probability that exactly 3 resign.
(a)0.493(b)0.083
(c)0.240(d)0.250
14.Find the probability that at most 3 three resign.
(a)0.493(b)0.507
(c)0.240(d)0.250
15.Find the mean, , of the probability distribution.
(a)40 employees(b)3.6 employees
(c)2.52 employees(d)1.59 employees
16.Find the standard deviation, , of the probability distribution.
(a)3.6 employees(b)2.52 employees
(c)1.59 employees(d)1.47 employees
17.Would it be unusual for 9 of the 12 employees to resign during the first year? Explain.
(a)Yes, because the probability of 9 or more people resigning is larger than 0.05.
(b)No, because the probability of 9 or more people resigning is less than 0.05.
(c)Yes, because 9 is higher than the maximum usual number of employees to resign.
(d)No, because 9 is lower than the maximum usual number of employees to resign.
18)If the odds for you are 1:3. what is the probability of winning?, losing?
19)How many ways can the letters of the word Massachusetts be arranged?
20) The expected value of a random variable represents the average value of the outcomes
of the random variable.
20)Winning the jackpot requires that you select the correct five numbers between 1 and 47
inclusive, in any order. What is the probability of winning if you purchase 3 tickets?