MAT121 Practice Exercises

Concepts of Probability

Instr. C. Peng

Please show your work before checking the answer and explanations. The exam questions will be similar to these exercise problems.


Problem 1.  When a quarter is tossed four times, 16 outcomes are possible.

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Here, for example, HTTH represents the outcome that the first toss is heads, the next two tosses are tails, and the fourth toss is heads. List the outcomes that comprise the following event.
Define event E = event exactly three tails are tossed.

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Problem 2.   In a competition, two people will be selected from four finalists to receive the first and second prizes. The prize winners will be selected by drawing names from a hat. The names of the four finalists are Jim, George, Helen, and Maggie. The possible outcomes can be represented as follows.

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Here, for example, JG represents the outcome that Jim receives the first prize and George receives the second prize. List the outcomes that comprise the following event.
A = event that Helen gets a prize


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Problem 3.   The age distribution of students at a community college is given below.

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A student from the community college is selected at random. The event A is defined as follows.
A = event the student is between 26 and 35 inclusive.
Determine the number of outcomes that comprise the event (not A).


A) 4441
B) 5294
C) 4220
D) 1926


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Problem 4.   A survey resulted in the sample data in the given table. If one of the survey respondents is randomly selected, find the probability of getting someone who lives in a flat.

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A) 424
B) 0.002
C) 0.393
D) 0.259


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Problem 5.   Suppose a coin is tossed four times. Let X denote the total number of tails obtained in the four tosses. What are the possible values of the random variable X?


A) 1, 2, 3
B) 0, 1, 2, 3, 4
C) HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT
D) 1, 2, 3, 4


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Problem 6.   For a randomly selected student in a particular high school, let Y denote the number of living grandparents of the student. Use random-variable notation to represent the event that the student obtained has exactly three living grandparents.


A) {Y >= 3} B) P{Y = 3} C) {Y < 3} D) {Y = 3}


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Problem 7.   When two balanced dice are rolled, 36 equally likely outcomes are possible as shown below.

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Let X denote the smaller of the two numbers. If both dice come up the same number, then X equals that common value. Find the probability distribution of X. Leave your probabilities in fraction form.


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Problem 8.   A statistics professor has office hours from 9:00 am to 10:00 am each day. The number of students 13) waiting to see the professor is a random variable, X, with the distribution shown in the table.

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The professor gives each student 10 minutes. Determine the probability that a student arriving just after 9:00 am will have to wait no longer than 30 minutes to see the professor.


A) 0.95
B) 0.25
C) 0.40
D) 0.80


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Problem 9.   The time taken to answer an exam question for a randomly chosen student has a uniform probability distribution from 1 minute to 5 minutes. What is the probability that the time to answer is no more than 2 minutes?


A. 0.20
B. 0.25
C. 0.40
D. 0.75


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Problem 10.   The time taken to deliver a pizza has a uniform probability distribution from 20 minutes to 60 minutes. What is the probability that the time to deliver a pizza is exactly 25 minutes?


A. 0.125 B. 0.300 C. 0.700 D. 0


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