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I. Find the probability of selecting four consecutive threes when four cards are drawn without
replacement from a standard deck of 52 playing cards. Round your answer to four decimal places .
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2. Find the probability of selecting four consecutive threes when four cards are drawn with replacement
from a standard deck of 52 playing cards. Round your answer to four decimal places.
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3. What is mutually exclusive?
The table lists the smoking habits of a group of college students.
Men
Woman
Total
Non-smoker
RegularSmoker
Heavy-smoker
Total
135
187
322
13
21
34
5
153
217
370
9
14
4. If a student is chosen at random, find the probability of getting someone who is a regular or heavy
smoker. Round your answer to three decimal places.
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5. Adelivery route must include stops at five cities. If the route is randomly selected, find the
probability that the cities will be arranged in alphabetical order.
6. The Chandler school board must visit nine schools for complaints of bugs. In how many different
ways can a member visit six of these to investigate this week?
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7. If a couple has px-ooys and three girls, how many gender sequences are possible?
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8. How many ways can seven people A, B, C, D, E, F, and G, sit in a row at a movie theater if A and B
must not sit by each ether?
f! - (&, ~ +<:o~)= '3"6D
9. How many ways can seven people A, B, C, D, E, F. and G, sit in a row at a movie theater if A and B
must sit by each other?
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10. Classify the event as dependent or independent.
peA and B) = 0.42
0.7):..
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Events A and B where peA) = 0.6, PCB) = 0.7 and
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II. Classify the event as dependent or independent. Events A and B ,where peA) = 0.6, P9B)=0.7
peA and B) = 0.38
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p( A ,y-...d e) -==t
P( ,4). PCb'J
and
.
Dependent Events:
Multiplication Rule
peA and B occurring) = P(A). PCBgiven that A has occurred)
peA and B)
= P(A).
p(BIA)
Independent Events: peA and B) = P(A). PCB)
12. Suppose a box contains 3 defective light bulbs and 12 good bulbs. Two bulbs are chosen from the
box without replacement. To fmd the probability that one of the bulbs drawn is good and one is
defective, which expression would you use?
12 11 3 2
12 3
12 3
3 2
12 3
e) _.-+-.a)-+b) _.-+-.c) _.IS 14 13 14
IS 14
IS IS IS IS
IS 14
13. Which of the following is true about dependent events?
a) p(AIB) = 0
b) p(AIB) = I
c) p(AIE) = A
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p(AIB)"# A
14. Identify why this assignment of probabilities carmot be legitimate: PA) = .4, PCB) = .3, peA and B) = .
.5.
a. A and B are not given as mutually exclusive events.
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peA and B) carmot be greater than either peA) or PCB).
c. The assignment is legitimate.
15. Which ofthe following events are mutually exclusive?
i. A = the sum of two dice is 7.
ii. B = the flip of a coin is a head.
iii. C = the sum of two dice is 11.
a) A and B
b) Band C
ecl A and C :::,
d) A, B, and C
il) No pair is mutually exclusive.
'Use the following information for question 5 - 6.
The probability of any person in your Student Council being selected for the Spring Dance Committee is 0.3;
the probability that a person on the Spring Dance committee is elected Chairperson of this committee is 0.2.
16. Find the probability that a member of the Student Council, chosen at random, is the Chairperson of
the committee.
a. 0.16
b. 0.85
c.. 0.89
d. 0.94
u:
None of these"':::>
17. Find the probability that a member of the Student Council, chosen at random, is 1lot the Chairperson
of the committee.
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a. 0.16
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e. None of these.
18. Find the probability of flipping a head on a coin and rolling a sum of 8 on two dice.
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19. A box contains II nickels, 4 dimes, and. 5 quarters. If you draw 3 coins at random from the box
without replacement, what is the probability that you will get a nickel, a dime, and a nickel in that
order?
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20. Find the probability of rolling two dice"and getting either a sum of 8 or both dice
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21. If an automobile license plate must consist of three letters followed by three single-digit numbers,
how many different license plates are possible? Remember that numbers and letters could be
duplicated.
10. /0 ~ 17, '57 <t> J OdD
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22. If a combination lock has a three-digit combination and the wheel on the lock allows any number
from 0 to 40, how many different combinations are possible? (Assume that numbers can repeat.)
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23. How many four-digit numbers have both the hundreds and units digits even?
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24. How many ways can we arrange a row of four girls followed by four boys if the girls must sit
together and boys must sit together?
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26. Do you notice the patterns of the pairs above in question 1"4? Equate each combination listed below
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