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Math 115
Exam 2
No Work-No Credit
Fall 05
Please circle your answer.
Name
Last 4 digits
1) If an event must occur, we assign it a probability of:
a) –1
b) 1
c) 0.50
d) 0
2) The expected value of a probability distribution is the same as the
a) mean.
b) standard deviation.
c) variance.
d) median.
3) If a random variable may take on any value then the random variable
is said to be
a) random.
b) discrete.
c) continuous.
d) disjoint.
4) The compliment of event A consists of
a) all elements in A.
b) all elements in A and not in A.
c) all elements not in A.
d) none of the above.
5) Two events are independent if
a) the occurrence of one leads to the occurrence of the other.
b) they cannot occur at the same time.
c) they must occur at the same time.
d) the occurrence of one does not affect the probability of the
occurrence of the other.
6) Two events are mutually exclusive if
a) the occurrence of one leads to the occurrence of the other.
b) they cannot occur at the same time.
c) they must occur at the same time.
d) the occurrence of one does not affect the probability of the
occurrence of the other.
7) A roulette wheel has 38 spaces numbered 1 through 36, 0, and 00.
Find the probability of
a) getting an odd number.
18
P(odd) =
38
b) a number less than 15 (not counting 0 and 00).
14
P(number < 15) =
36
8) In an English class there are 18 juniors and 10 seniors: 6 of the seniors
are female and 12 of the juniors are male. If a student is selected at
random find the probability of selecting a senior or a female.
P(senior or female) = P(S) + P(f) – P(S and f) =
10 12
6
16
+
−
=
28 28 28 28
9) Three cable channels (6, 8 or 10) have quiz shows, comedies, and dramas.
The number of each is shown in the table.
Type of show
Channel 6 Channel 8
Channel 10
Quiz Show
5
2
1
Comedy
3
2
8
Drama
4
4
2
If a show is selected at random, find the probability that:
a) the show is a quiz show or the show is on channel 8.
8 8
2 14
+
−
=
P(quiz or on ch. 8) = P(q) + P(ch8) – P(q and ch8) =
31 31 31 31
b) the show is a comedy or a drama.
P(comedy or drama) = P(c) + P(d) – P(c and d) =
13 10
23
+ −0=
31 31
31
10) Three cards are drawn from an ordinary deck of cards and not replaced.
Find the probability of
a) getting three kings.
24
⎛ 4 ⎞⎛ 3 ⎞⎛ 2 ⎞
≈ 0.000181 .
P(King and king and king) = ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ =
⎝ 52 ⎠ ⎝ 51 ⎠ ⎝ 50 ⎠ 132600
b) getting three hearts.
1716
⎛ 13 ⎞ ⎛ 12 ⎞ ⎛ 11 ⎞
≈ 0.0129 .
P(heart and heart and heart) = ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ =
132600
⎝ 52 ⎠ ⎝ 51 ⎠ ⎝ 50 ⎠
11) A coin is tossed five times. Find the probability of getting at least 1 tail.
P(at least 1 tail) = 1 – P(no tails) = 1 -
1
31
.
=
32 32
12) A flashlight has 8 batteries, two of which are defective. If two are
selected without replacement, find the probability that both are
defective.
2
⎛ 2 ⎞⎛ 1 ⎞
.
P(both duds) = ⎜ ⎟ ⎜ ⎟ =
⎝ 8 ⎠ ⎝ 7 ⎠ 56
⎛
13) Given this probability distribution ⎜ µ = ∑ xP( x), σ =
⎜
⎝
x
x2
P(x)
3
1
1
10
3
3
9
10
4
5
25
10
a) determine the mean, µ
µ=
32
= 3.2
10
xP(x)
3
10
9
10
20
10
∑ x P( x) − µ
2
x2P(x)
3
10
27
10
10
b) standard deviation, σ
σ = 13 − 3.22 ≈ 1.661
2
⎞
⎟⎟
⎠
14) From a sample of 9 children, 60% had chicken pox by the time they were
12 years old. Find the probability that
a) exactly seven have had the chicken pox.
P(x = 7) = 0.161
b) no more than 4 have had the chicken pox.
P(x ≤ 4) = 0 + 0.004 + 0.021 + 0.074 + 0.167 = 0.266.
15) A survey found that 63% of Americans said they own an answering
machine. If 14 Americans are selected at random, find the probability that
a) exactly 10 own an answering machine.
P(x = 10) =
C10 ( 0.63)
10
14
( 0.37 )
4
≈ 0.185
b) at least 12 own an answering machine.
P ( x ≥ 12) = P ( x = 12) + P ( x = 13) + P ( x = 14) =
C12 ( 0.63)
12
14
( 0.37 )
2
+
C13 ( 0.63)
13
14
( 0.37 ) + 14 C14 ( 0.63) ( 0.37 )
14
0
≈ 0.063.
c) From a sample of 14, how many Americans would you expect to have an
answering machine.
µ = np = (14 )( 0.63) = 8.82 .