During the morning commute to work, a person has to cross 20 traffic lights. if the...
During the morning commute to work, a person has to cross 20 traffic lights. if the probability that each traffic light is green as the person approaches that traffic light is 0.2, determine the following:
a. the probability of finding exactly 5 traffic lights green during the commute.
b. the probability of finding the number of traffic lights green during the commute lies between 3 and 6.
Homework Answers
Note
that this probability is calculated inclusive.Add Answer to:
During the morning commute to work, a person has to cross 20
traffic lights. if the...
A particularly long traffic light on your morning commute is green 40% of the time that...
A particularly long traffic light on your morning commute is green 40% of the time that you approach it. Assume that each morning represents an independent trial. Let denote the number of mornings the light is green. a) Over 10 mornings, what is the probability that the light is green on exactly 4 days? Round your answer to three decimal places (e.g. 98.765) b) Over 20 mornings, what is the probability that the light is green on exactly 8 days?...
5. Use the propenties of the gamma function to t( poimts a. (a) r(S) (b) rz) 6 A long traffic light on your morning commute is green 20% of the time that you approach it. Assume that cach morning...
5. Use the propenties of the gamma function to t( poimts a. (a) r(S) (b) rz) 6 A long traffic light on your morning commute is green 20% of the time that you approach it. Assume that cach morning represents an independent r [10 points (a) Over 5 morning, what is the probability that the light is green on exactly one day? (b) Over 20 mornings, what is the probability that the light is green on exactly four days? 7....
A particu arly ong traffic ght on your morning commute is green 10% o the time...
A particu arly ong traffic ght on your morning commute is green 10% o the time that you approach t Assume hat each morn ng represents an independent na Let denote the number o mornings he ght is green. a) Over 10 mornings, what is the probability that the light is green on exactly 1 day? Round your answer to three decimal places (e.g. 98.765) P 38.742 b) Over 20 mornings, what is the probability that the light is green...
A driver encounters two traffic lights
A driver encounters two traffic lights on the way to work each morning. Each light is either red, yellow, or green. The probabilities of the various combinationsof colors is given in the followingtable:Second lightFirst LightRYGR0.300.040.16Y0.050.010.04G0.150.050.20a. What is the probability the first light is red?b. What is the probability that the second light is green?c. Find the probability that both lights are the same color.d. Given that the first light is red, find the probability that the second light is green.e....
2. Consider the following problem associated with synchronizing traffic lights. A particular traffic light (Light A)...
2. Consider the following problem associated with synchronizing traffic lights. A particular traffic light (Light A) has a cycle as follows: Red = 1 min Green = 1.5 min Yellow = 0.5 min Some distance before Light A is another light (Light B). Due to varying drivers and conditions, the travel time between the two lights varies from vehicle to vehicle. Data suggest that 40% of all cars leaving Light B at a time when Light A is red are...
9. (25 points) George keeps track of how often he makes it through stop lights on...
9. (25 points) George keeps track of how often he makes it through stop lights on his way to work every morning and how many times he has to stop. Assume that whether or not he makes it through one light is independent of whether or not he makes it through the next light (there are some reasons why they might not be independent, but for this problem, you can assume that they are). According to George's records, he makes...
A commuter must pass through five traffic lights on her way to work, and she will...
A commuter must pass through five traffic lights on her way to work, and she will have to stop at each one that is red. After years of commuting she has developed the following probability distribution for the number of red lights she stops at each day on her way to work: No. of red lights x 0 1 2 3 4 5 Probability .05 .25 .30 .20 .15 .05 Note that the standard deviation of the above probability distribution...
A commuter must pass through five traffic lights on her way to work, and she will...
A commuter must pass through five traffic lights on her way to work, and she will have to stop at each one that is red. After years of commuting she has developed the following probability distribution for the number of red lights she stops at each day on her way to work No. of red lights Probability o 1 2 3 4 5 OS 25 30 30.5 TOS Note that the standard deviation of the above probability distribution is SDX)...
There are two traffic lights on Darlene's route from home to work. Let E denote the...
There are two traffic lights on Darlene's route from home to work. Let E denote the event that Darlene must stop at the first light, and define the event Fin a similar manner for the second light. Suppose that P(E) = 0.3, P(F) = 0.2, and P(En F) = 0.15. (a) What is the probability that Darlene must stop at at least one light; that is, what is the probability of the event P(EU F)? (b) What is the probability...
Question 24 1 pts If there are two traffic lights between your house and your office,...
Question 24 1 pts If there are two traffic lights between your house and your office, what is the probability that you will have two green lights on the way to work? Assume that each element of the sample space is equally likely to occur. Hint: The sample space is S (GG, GR, RG, RR, where G represents a green light and R represents a red light. .25 ○ .1 。75
5. Use the propenties of the gamma function to t( poimts a. (a) r(S) (b) rz) 6 A long traffic light on your morning commute is green 20% of the time that you approach it. Assume that cach morning represents an independent r [10 points (a) Over 5 morning, what is the probability that the light is green on exactly one day? (b) Over 20 mornings, what is the probability that the light is green on exactly four days? 7....
A particu arly ong traffic ght on your morning commute is green 10% o the time that you approach t Assume hat each morn ng represents an independent na Let denote the number o mornings he ght is green. a) Over 10 mornings, what is the probability that the light is green on exactly 1 day? Round your answer to three decimal places (e.g. 98.765) P 38.742 b) Over 20 mornings, what is the probability that the light is green...
A driver encounters two traffic lights on the way to work each morning. Each light is either red, yellow, or green. The probabilities of the various combinationsof colors is given in the followingtable:Second lightFirst LightRYGR0.300.040.16Y0.050.010.04G0.150.050.20a. What is the probability the first light is red?b. What is the probability that the second light is green?c. Find the probability that both lights are the same color.d. Given that the first light is red, find the probability that the second light is green.e....
2. Consider the following problem associated with synchronizing traffic lights. A particular traffic light (Light A) has a cycle as follows: Red = 1 min Green = 1.5 min Yellow = 0.5 min Some distance before Light A is another light (Light B). Due to varying drivers and conditions, the travel time between the two lights varies from vehicle to vehicle. Data suggest that 40% of all cars leaving Light B at a time when Light A is red are...
9. (25 points) George keeps track of how often he makes it through stop lights on his way to work every morning and how many times he has to stop. Assume that whether or not he makes it through one light is independent of whether or not he makes it through the next light (there are some reasons why they might not be independent, but for this problem, you can assume that they are). According to George's records, he makes...
A commuter must pass through five traffic lights on her way to work, and she will have to stop at each one that is red. After years of commuting she has developed the following probability distribution for the number of red lights she stops at each day on her way to work No. of red lights Probability o 1 2 3 4 5 OS 25 30 30.5 TOS Note that the standard deviation of the above probability distribution is SDX)...
There are two traffic lights on Darlene's route from home to work. Let E denote the event that Darlene must stop at the first light, and define the event Fin a similar manner for the second light. Suppose that P(E) = 0.3, P(F) = 0.2, and P(En F) = 0.15. (a) What is the probability that Darlene must stop at at least one light; that is, what is the probability of the event P(EU F)? (b) What is the probability...
Question 24 1 pts If there are two traffic lights between your house and your office, what is the probability that you will have two green lights on the way to work? Assume that each element of the sample space is equally likely to occur. Hint: The sample space is S (GG, GR, RG, RR, where G represents a green light and R represents a red light. .25 ○ .1 。75
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