Imagine a game show on television where one lucky contestant is presented with three upside-down buckets that are numbered 1, 2, and 3. Under one of the buckets is a five-ounce gold bar. Under each of the other two buckets is a lump of coal. After the game ends, the contestant receives what is under his or her bucket. The host of the game show asks the contestant to choose one of the three buckets. After the contestant makes a choice, the host lifts up one of the remaining two buckets to reveal a lump of coal under it. At this point, only two buckets remain uncovered: the bucket that the contestant originally chose and the bucket that was not uncovered by the host. The host subsequently asks the contestant if he or she would like to keep the original bucket or change buckets to the only other bucket remaining. 1. If the contestant does not change buckets and stays with the original bucket chosen, what is the probability that the contestant will win the five-ounce gold bar? ( Select] 2. If the contestant does not change buckets and stays with the original bucket chosen, what is the probability that the contestant will win a lump of coal? (Select 1 3. If the contestant changes buckets from the original bucket to the other bucket remaining, what is the probability that the contestant will win the five-ounce gold bar? [ Select) 4. If the contestant changes buckets from the original bucket to the other bucket remaining, what is the probability that the contestant will win a lump of coal? [Select]
Imagine a game show on television where one lucky contestant is presented with three upside-down buckets that are numbered 1, 2, and 3. Under one of the buckets is a five-ounce gold bar. Under each of the other two buckets is a lump of coal. After the game ends, the contestant receives what is under his or her bucket. The host of the game show asks the contestant to choose one of the three buckets. After the contestant makes a choice, the host lifts up one of the remaining two buckets to reveal a lump of coal under it. At this point, only two buckets remain uncovered: the bucket that the contestant originally chose and the bucket that was not uncovered by the host. The host subsequently asks the contestant if he or she would like to keep the original bucket or change buckets to the only other bucket remaining. 1. If the contestant does not change buckets and stays with the original bucket chosen, what is the probability that the contestant will win the five-ounce gold bar? ( Select] 2. If the contestant does not change buckets and stays with the original bucket chosen, what is the probability that the contestant will win a lump of coal? (Select 1 3. If the contestant changes buckets from the original bucket to the other bucket remaining, what is the probability that the contestant will win the five-ounce gold bar? [ Select) 4. If the contestant changes buckets from the original bucket to the other bucket remaining, what is the probability that the contestant will win a lump of coal? [Select]
Chapter9: Sequences, Probability And Counting Theory
Section9.5: Counting Principles
Problem 40SE: A family consisting of 2 parents and 3 children is to pose for a picture with 2 family members in...
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![Imagine a game show on television where one lucky contestant is presented with three upside-down
buckets that are numbered 1, 2, and 3. Under one of the buckets is a five-ounce gold bar. Under each of
the other two buckets is a lump of coal. After the game ends, the contestant receives what is under his or
her bucket.
The host of the game show asks the contestant to choose one of the three buckets. After the contestant
makes a choice, the host lifts up one of the remaining two buckets to reveal a lump of coal under it. At
this point, only two buckets remain uncovered: the bucket that the contestant originally chose and the
bucket that was not uncovered by the host.
The host subsequently asks the contestant if he or she would like to keep the original bucket or change
buckets to the only other bucket remaining.
1. If the contestant does not change buckets and stays with the original bucket chosen, what is the
probability that the contestant will win the five-ounce gold bar? [Select]
2. If the contestant does not change buckets and stays with the original bucket chosen, what is the
probability that the contestant will win a lump of coal? [Select
3. If the contestant changes buckets from the original bucket to the other bucket remaining, what is
the probability that the contestant will win the five-ounce gold bar?
[ Select )
4. If the contestant changes buckets from the original bucket to the other bucket remaining, what is
the probability that the contestant will win a lump of coal? [ Select]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F022654e1-be4a-45b5-b233-3d8dac2643d3%2F7ef03063-e4a3-4b3b-ad84-3044760b60ed%2Fp8vd7o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Imagine a game show on television where one lucky contestant is presented with three upside-down
buckets that are numbered 1, 2, and 3. Under one of the buckets is a five-ounce gold bar. Under each of
the other two buckets is a lump of coal. After the game ends, the contestant receives what is under his or
her bucket.
The host of the game show asks the contestant to choose one of the three buckets. After the contestant
makes a choice, the host lifts up one of the remaining two buckets to reveal a lump of coal under it. At
this point, only two buckets remain uncovered: the bucket that the contestant originally chose and the
bucket that was not uncovered by the host.
The host subsequently asks the contestant if he or she would like to keep the original bucket or change
buckets to the only other bucket remaining.
1. If the contestant does not change buckets and stays with the original bucket chosen, what is the
probability that the contestant will win the five-ounce gold bar? [Select]
2. If the contestant does not change buckets and stays with the original bucket chosen, what is the
probability that the contestant will win a lump of coal? [Select
3. If the contestant changes buckets from the original bucket to the other bucket remaining, what is
the probability that the contestant will win the five-ounce gold bar?
[ Select )
4. If the contestant changes buckets from the original bucket to the other bucket remaining, what is
the probability that the contestant will win a lump of coal? [ Select]
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