MATH 227
1.
TEST#2(CH.4)
SOLUTIONS
FALL 2013
3 pts
If the probability that we’ll have a storm this Friday is 0.10, what is the
probability that we will not have a storm this Friday?
𝑃(𝑅̅ ) = 1 − 0.10 = 0.90,
2.
5 pts
The greater Cincinnati airport led major U.S. airports in on-time arrivals in the
last quarter of 2005 with an 84.3% on-time rate. Choose 5 arrivals at random and find the
probability that at least 1 was not on time.
P(at least one not on time)  1  P(none not on time)
 1  P(all 5 on time)  1  (0.843)5  0.574
3.
6 pts
State which events are independent and which are dependent.
a) Tossing a coin and drawing a card from a deck
b) Driving on ice and having an accident
Independent
Dependent
c) Smoking excessively and having lung cancer Dependent
4.
5 pts
There are 9 members on the board of directors for a hospital. If they must elect a
chairperson, vice chairperson, and a secretary, how many different slates of candidates
are possible?
9
5.
P2  ...... Order matters because we have different positions
6 pts
If 2 cards are selected from a standard deck of 52 cards without replacement, find
these probabilities.
a) Both cards are diamond
P (Both are diamond) =P (1st is a diamond) * P (2nd is a diamond) =
(13/52)*(12/51) = ……
b) One card is club and one card is diamond
P (One club and one diamond) = (13/52)*(13/51) = ….
6 pts
6.
It is reported that only 27% of U.S. adults get enough leisure time exercise to
achieve cardiovascular fitness. Choose 3 adults at random. Find the probability that
a) All 3 adults get enough exercise
P(all 3 get enough exercise) = (0.27)3 =0.0197
b) At least one adult gets enough exercise
P(at least one gets enough exercise) = 1-(0.73)3 =0.611
13 pts
7.
Evaluate the expression: You know how to calculate this….
C3
5 C4
c) 9 P8
d) 5 P5
e) 5 !
a)
b)
8
8.
4 pts
9.
4 pts
Determine whether these events are mutually exclusive.
a) Roll a die: Get a number greater than 3, and get a number less than 3. Yes
b) Select a registered voter: The voter is a Republican, and the voter is a Democrat. Yes
At a convention there are 10 mathematics instructors, 4 electrical engineering
instructors, 6 statistics instructors, and 4 science instructors. If an instructor is selected,
find the probability of getting a mathematics instructor or a science instructor.
𝑃(𝑚𝑎𝑡ℎ 𝑜𝑟 𝑠𝑐𝑖𝑒𝑛𝑐𝑒) =
10 4
14
+
=
24 24 24
10. If two dice are rolled one time, find the probability of getting these
results.
a)
5 pts
A sum of 8.
Before we start, let’s find the sample space
If you roll two dice, the
Sample Space is {(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),
(2,1),(2,2),(2,3),(2,4),(2,5), (2,6),
…………………………………..
(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}  36 possibilities
Those who have the sum of 8 are {(2,6),(3,5),(4,4),(5,3),(6,2)}  That’s 5
P(a sum of 8)=
b)
4 pts
5
36
A sum greater than 10.
{(5,6),(6,5),(6,6)}
3
1

P(sum >10)=
36 12
c)
5 pts
A sum less than or equal to 4.
6
1
𝑃(sum ≤ 4) = 36 = 6 ,
{(1,1), (1,2), (2,1), (1,3), (3,1), (2,2)}
11. The table below describes the smoking habits of a group of asthma sufferers.
Nonsmokers Occasional Regular Heavy
Total
Smoker
smoker
smoker
Men
339
33
61
34
467
Women 377
32
84
36
529
Total
716
65
145
70
996
If one of the 996 people is randomly selected, find the probability of:
a)
b)
3 pts
4 pts
getting a regular or heavy smoker. Answer: 0.216
getting a woman or a regular smoker. (529/996)+(145/996)-
(84/996)=0.5923
12. The medal distribution from the 2004 Summer Olympic Games for the top 23 countries is
shown below.
Gold
Silver
Bronze
Total
United States
35
39
29
103
Russia
27
27
38
92
China
32
17
14
63
Australia
17
16
16
49
Others
133
136
153
422
Total
244
235
250
729
Choose one medal winner at random.
a)
4 pts
Find the probability that the winner won the gold medal, given that the winner
was from the United States.
35
P( gold medal and from U .S ) 729
P( gold medal | United States) 

 0.340
103
P( from U .S )
729
b)
4 pts
Find the probability that the winner was from the United States, given that she or
he won a gold medal.
35
P(U .S and gold medal ) 729
P( from U .S | gold medal ) 

 0.143
244
P( gold medal )
729
13. 9 pts A box has 12 calculators, 4 of which are defective. If we randomly select 4
calculators, find the probability of getting.
a) 1 defective calculator.
You are selecting 4 calculators out of 12 calculators  combination (order does not
matter)
4
C1 8 C3
 ........
12 C 4
b) 0 defective calculators.
C4
 ........
12 C 4
8
c) 3 defective calculators.
4
C3 8 C1
 ........
12 C 4
14. 6 pts How many different 4-digit identification tags can be made if the digits can be
used more than once? If repetitions are not permitted?
𝑎) 10 ∗ 10 ∗ 10 ∗ 10 = 10000, 𝑤𝑖𝑡ℎ 𝑟𝑒𝑝𝑒𝑎𝑡𝑠
b)10 * 9 * 8 * 7 = ….
15. 4 pts How many different ways can 6 different books be arranged on a shelf?
6!=……..