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MATH 2280 TEST PRACTICE 2
Name:__________________________
1. Maggie watched 100 cars drive by her window and compiled the following data:
Model Number
Ford
23
Toyota
25
GM
18
Chrysler
17
Honda
17
What is the empirical probability that the next car is
(a) A Ford?
(b) Not a Toyota?
(c) A Chrysler or a GM?
(d) A Rolls Royce?
2. In a class of 100 students, 75 take statistics, 21 take calculus and 13 take both subjects.
What is the probability that a randomly selected student takes neither statistics nor
calculus?
3. In an English class there 12 juniors and 15 seniors; 7 of the juniors are males and 5 of
the seniors are females. If a student is selected at random, find the probability of
selecting the following:
(a) A senior or a female
(b) A junior or a senior
4. In an election 47% of eligible voters did not vote. If three eligible voters are selected
at random find:
(a) The probability that none of them voted in the election.
(b) The probability that at least one of the three voted in the election.
5. If two cards are selected from a 52 card deck without replacement, find these
probabilities:
(a) Both are kings
(b) The cards are different suits
6. At a small college, the probability that a student takes physics and sociology is 0.18.
The probability that a student takes sociology is 0.72. Find the probability that a student
is taking physics, given that he is taking sociology. To get credit you must show the
formula you use to get your answer.
7. In a board of directors composed of eight people, in how many ways can one chief
executive officer, one director, and one treasurer be selected?
8. In how many ways can a committee of four people be selected from a pool of ten
people?
9. In how many ways can a jury of six women and six men be selected from nine women
and twelve men?
10. A bag contains five red balls and seven white balls. If you select four balls at
random without replacement, find the probability that you get two red balls and two
white balls.
11. A box contains four $1 bills, five $5 bills, one $10 bill and six $100 bills. Construct
a probability distribution for the experiment of selecting one bill at random from the box.
12. Find the mean, variance and standard deviation for the distribution shown.
X
1
2
3
4
5
P( X ) 0.3 0.15 0.36 0.12 0.07
13. Dogdale College needs to raise money to buy a computer. They decide to conduct a
raffle. A cash prize of $4,000 is to be awarded. If they sell 3,000 tickets at $3 each find
the expected gain if you buy one ticket. (There will be only one winning ticket.) You
must set up a probability distribution to get credit.
14. A fair die is rolled 12 times. Let X be the number of threes in the twelve rolls. Find
the following probabilities.
(a) P( X  3)
(b) P( X  4)
(c) P( X  7)