Period
Name
Special Topics Homework
Section 8.1
Day 2
1)
Suppose a box contains 3 defective light bulbs and 12 good bulbs. Two bulbs are chosen from the
box without replacement. Wha!!s tle p!oibabilitythat oneof two bulbs drawn is defective and,,
one
2)
is
not?
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The probability of rain on Monday is .3 and on Thursday is .4. Assuming these are independent,
what is the probability that
a) it rains on both days?
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b) it does not rain on Monday? i"
c) it rains on Monday, but not Thursday? ÿ .!;ÿ ÿi. ÿ ).- j ÿ ÿ"
d) it rains on at least one of these days? +, ÿ::;: /, :/:1 <: ÿ Si
e) it doesn't rain on either day? ,÷, /:ii '/<iÿ" /::ÿ'ÿ "/" ......... "
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3)
One card is randomly selected from a standard 52-card deck. Find the probability that the card is
an ace or a black card.
A. 1/26 ........-ÿ-'ÿ"ÿ,,
b. 15/26
E. 112
4)
Which of the following pairs of events are disjoint (mutually exclusive)?
F.
A: the odd numbers; B: the number 5
G.
A: the even numbers; B: the numbers greater than 10
H,
A: the numbers less than 5; B: all negative numbers
A: the numbers above 100; B: the numbers less than -200
J,
5)
A: negative numbers; B: odd numbers
You flip four coins. What's the probability of getting exactly two heads?
K. 1/8
L. 5/8
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[
M. 318 ÿ>
N. 114
o. 11/16
6)
Based on Census Bureau definitions, select an American household at random and let A
represent the event that the selected household is prosperous (income > $75000) and B
represent the event that the household is educated (householder completed college). The
Census Bureau states that P (A) = 0.125, P (B) = 0.237, and P (A and B) = .077. What is the
probability that the household selected is prosperous or educated?
2,
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7)
A deck of 52 cards are shuffled well and 3 cards are drawn with replacement. What is the
probability that you will get two black cards and one red card or thaÿt/you will get two red cards
and one black card? l;j { ;:;iJt;;..:i; )
8)
'° "Y" ;'
Two events, A and B, are such that P(A) = .45, and P(A and B) = .28. If A and B are independent,
find:
a)
b)
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ÿ
:
P(B) = ÿ,ÿ
P(Aor B)-- . ; "/ÿ
9)
Police report that 78% of drivers stopped on suspicion of drunk driving are given a breath test,
36% a blood test, and 22% both tests. What is the probability that a randomly selected driver
suspected of drunk driving is given a blood test or a breath test?
i0
A general can plan a campaign to fight one major battle or three small battles. He believes he
has a probability of 0.6 of winning the large battle and a probability of 0.8 of winning each of the
small battles. Victories or defeats in the small battles are independent. The general must win
either the large battle or all three of the smaller battles to win the campaign. Which
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strategy should he choose?
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Jeanie is a bit forgetful, and if she doesn't make a "to do" list, the probability thai" she
forgets something she is supposed to do is .1. Tomorrow she intends to run three errands, and
she fails to write them on her list.
a. What is the probability that Jeanie forgets all three errands?
.
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b. What is the probability that Jeanie forgets at least one of the three errands? ÿ;
c. What is the probability that Jeanie remembers the first errand but not the second or third?(
12.
Many fire stations handle emergency calls for medical assistance as well as calls requesting fire-
fighting equipment. A particular station says that ?he probability that an incoming call is for
medical assistance is .85.
a, What is the probability that a call is not for medical assistance? .,,
b. Assuming that successive calls are independent, what is the probability that both of two
successive calls will be for medical assistance? + / <q
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assistance?
c. What is the probability that three consecutive calls are not for medical
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d. What is the probability thaÿgf thenext 10 calls, at least one is for medical assistance?
13.
If you eat at Silly Bob's Cafe there's a 40% chance that your food will be cold and a 30%
chance your food will taste bad. Assume that these two events are independent.
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a. What is the probability that botÿ will occur, you food is cold ..dÿit
b. What is the probability that your food is cold or it tastes bad?
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14.
Andrew is 55, and the probability that he will be alive in 10 years is 0.72. Ellen is 35, and the
probability that she will be alive in 10 years is 0.92. Assuming that the life span of one will have
no effect on the life span of the other, what is the probability they will both be alive in 10 years?
15. Use the diagram for the following four questions.
At Mathis Cool High, the two primary school activities student participate in are student.council and math
club. The Venn below details the proportion of students involved in each activity.
A
B
S
A = involved in student council B = involved in math club
Given the diagram, what is the probability that a student selected at random will not participate in
either activity?
(A) .04
.
; (C).29
(b) .41
(E) 71
Given the diagram, what is the probability that a student selected at random will participate in student
council or in math club?
(A) .04
,
(B) .26
(B) .26
(C) .29
(b) .41
iE) .71 ;
If four consecutive students selected at random, what are the chances all four will participate in both
clubs?
/ (A) about 0% (B) 2.56% (C) 4%
(b) ÿ2%
(e)
25.4%
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