At fast one of these diseases in fact carry both of them. If a randomly selected tick is found to have carried HGE, what is the probability that the selected tick is also a carrier of Lyme disease? 56. For any events A and B with P(B) > 0, show that P(A|B) + P(A|B) = 1. 57. If P(BA)> P(B), show that P(B' |A) < P(B'). [Hint: Add P(B' A) to both sides of the given inequality and then use the result of Exercise 56.] 58. Show that for any three events A, B, and C with P(C) > 0, P(A UB|C) = P(A|C) + P(B|C) - P(A B|C). 59. At a certain gas station, 40% of the customers use regular gas (A₁), 35% use plus gas (A2), and 25% use premium (A3). Of those customers using regular gas, only 30% fill their tanks (event B). Of those customers using plus, 60% fill their tanks, whereas of those using premium, 50% fill their tanks. a. What is the probability that the next customer will request plus gas and fill the tank (A₂n B)? b. What is the probability that the next customer fills the tank? c. If the next customer fills the tank, what is the probability that regular gas is requested? Plus? Premium? 60. Seventy percent of the light aircraft that disappear while in flight in a certain country are subsequently discov- ered. Of the aircraft that are discovered, 60% have an emergency locator, whereas 90% of the aircraft not discovered do not have such a locator. Suppose a light aircraft has disappeared. a. If it has an emergency locator, what is the probability that it will not be discovered? b. If it does not have an emergency locator, what is the probability that it will be discovered? 61. Components of a certain type are shipped to a supplier in batches of ten. that 50% Thi 63. For tain era tha eve rar P( PC PC a. b. c. d. e. 64. TI de sh lo 60 10 L: 50 re do a. b.
At fast one of these diseases in fact carry both of them. If a randomly selected tick is found to have carried HGE, what is the probability that the selected tick is also a carrier of Lyme disease? 56. For any events A and B with P(B) > 0, show that P(A|B) + P(A|B) = 1. 57. If P(BA)> P(B), show that P(B' |A) < P(B'). [Hint: Add P(B' A) to both sides of the given inequality and then use the result of Exercise 56.] 58. Show that for any three events A, B, and C with P(C) > 0, P(A UB|C) = P(A|C) + P(B|C) - P(A B|C). 59. At a certain gas station, 40% of the customers use regular gas (A₁), 35% use plus gas (A2), and 25% use premium (A3). Of those customers using regular gas, only 30% fill their tanks (event B). Of those customers using plus, 60% fill their tanks, whereas of those using premium, 50% fill their tanks. a. What is the probability that the next customer will request plus gas and fill the tank (A₂n B)? b. What is the probability that the next customer fills the tank? c. If the next customer fills the tank, what is the probability that regular gas is requested? Plus? Premium? 60. Seventy percent of the light aircraft that disappear while in flight in a certain country are subsequently discov- ered. Of the aircraft that are discovered, 60% have an emergency locator, whereas 90% of the aircraft not discovered do not have such a locator. Suppose a light aircraft has disappeared. a. If it has an emergency locator, what is the probability that it will not be discovered? b. If it does not have an emergency locator, what is the probability that it will be discovered? 61. Components of a certain type are shipped to a supplier in batches of ten. that 50% Thi 63. For tain era tha eve rar P( PC PC a. b. c. d. e. 64. TI de sh lo 60 10 L: 50 re do a. b.
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.3: Binomial Probability
Problem 2E: If a binomial experiment has probability p success, then the probability of failure is...
Related questions
Question
59. At a certain gas station, 40% of the customers use regular gas (A1), 35% use plus gas (A2), and 25% use premium (A3). Of those customers using regular gas, only 30% fill their tanks (event B). Of those customers using plus, 60% fill their tanks, whereas of those using premium, 50% fill their tanks.
a. What is the probability that the next customer will request plus gas and fill the tank (A2 B)?
b. What is the probability that the next customer fills the tank?
c. If the next customer fills the tank, what is the probability that regular gas is requested? Plus? Premium?
![At fast one of these diseases in fact
carry both of them. If a randomly selected tick is found
to have carried HGE, what is the probability that the
selected tick is also a carrier of Lyme disease?
56. For any events A and B with P(B) > 0, show that
P(A|B) + P(A|B) = 1.
57. If P(BA)> P(B), show that P(B' |A) < P(B'). [Hint:
Add P(B' A) to both sides of the given inequality and
then use the result of Exercise 56.]
58. Show that for any three events A, B, and C with P(C) > 0,
P(A UB|C) = P(A|C) + P(B|C) - P(A B|C).
59. At a certain gas station, 40% of the customers use regular
gas (A₁), 35% use plus gas (A2), and 25% use premium
(A3). Of those customers using regular gas, only 30% fill
their tanks (event B). Of those customers using plus, 60%
fill their tanks, whereas of those using premium, 50% fill
their tanks.
a. What is the probability that the next customer will
request plus gas and fill the tank (A₂n B)?
b. What is the probability that the next customer fills
the tank?
c. If the next customer fills the tank, what is the
probability that regular gas is requested? Plus?
Premium?
60. Seventy percent of the light aircraft that disappear while
in flight in a certain country are subsequently discov-
ered. Of the aircraft that are discovered, 60% have an
emergency locator, whereas 90% of the aircraft not
discovered do not have such a locator. Suppose a light
aircraft has disappeared.
a. If it has an emergency locator, what is the probability
that it will not be discovered?
b. If it does not have an emergency locator, what is the
probability that it will be discovered?
61. Components of a certain type are shipped to a supplier in
batches of ten.
that 50%
Thi
63. For
tain
era
tha
eve
rar
P(
PC
PC
a.
b.
c.
d.
e.
64. TI
de
sh
lo
60
10
L:
50
re
do
a.
b.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff608d3a0-7ad6-4d87-98f1-9a851954d279%2F35c75b9c-408f-4288-96f3-6c496120d798%2Fo0p92s9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:At fast one of these diseases in fact
carry both of them. If a randomly selected tick is found
to have carried HGE, what is the probability that the
selected tick is also a carrier of Lyme disease?
56. For any events A and B with P(B) > 0, show that
P(A|B) + P(A|B) = 1.
57. If P(BA)> P(B), show that P(B' |A) < P(B'). [Hint:
Add P(B' A) to both sides of the given inequality and
then use the result of Exercise 56.]
58. Show that for any three events A, B, and C with P(C) > 0,
P(A UB|C) = P(A|C) + P(B|C) - P(A B|C).
59. At a certain gas station, 40% of the customers use regular
gas (A₁), 35% use plus gas (A2), and 25% use premium
(A3). Of those customers using regular gas, only 30% fill
their tanks (event B). Of those customers using plus, 60%
fill their tanks, whereas of those using premium, 50% fill
their tanks.
a. What is the probability that the next customer will
request plus gas and fill the tank (A₂n B)?
b. What is the probability that the next customer fills
the tank?
c. If the next customer fills the tank, what is the
probability that regular gas is requested? Plus?
Premium?
60. Seventy percent of the light aircraft that disappear while
in flight in a certain country are subsequently discov-
ered. Of the aircraft that are discovered, 60% have an
emergency locator, whereas 90% of the aircraft not
discovered do not have such a locator. Suppose a light
aircraft has disappeared.
a. If it has an emergency locator, what is the probability
that it will not be discovered?
b. If it does not have an emergency locator, what is the
probability that it will be discovered?
61. Components of a certain type are shipped to a supplier in
batches of ten.
that 50%
Thi
63. For
tain
era
tha
eve
rar
P(
PC
PC
a.
b.
c.
d.
e.
64. TI
de
sh
lo
60
10
L:
50
re
do
a.
b.
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