A daily commuter crosses two traffic signals on his way to work. The probability that he...

A daily commuter crosses two traffic signals on his way to work. The probability that he will be stopped at the first signal is 0.47, at the second signal is 0.30, and the probability that he may not have to stop at any of the two signals is 0.3. Answer all the questions to 2 decimal places where appropriate.

1. What is the probability that the commuter will be stopped at both signals?

2. What is the probability that he will be stopped at the second, but not at the first signal?

3. What is the probability that he will be stopped at exactly one signal given that he was not stopped at the first signal?

4. "Stopping at signal 1 is independent of stopping at signal 2." This statement is:
a.Incorrect True because P(stopping at both signals) = P(stopping at signal 1)×P(stopping at signal )
b.ncorrect False because P(stopping at both signals) ≠ 0
c.Incorrect True because P(stopping at both signals) ≠ 0
d.Correct: False because P(stopping at both signals) ≠ P(stopping at signal 1)×P(stopping at signal 2)

Solutions

Expert Solution

orchestra answered 1 year ago

Next > < Previous

Related Solutions

A commuter must pass through five traffic lights on her way to work and will have...

A commuter must pass through five traffic lights on her way to work and will have to stop at each one that is red. She estimates the probability model for the number of red lights she hits (x), as shown below: x 0 1 2 3 4 5 p(x) 0.04 0.23 p 0.1 0.1 0.1 a)Find the probability that she hits at most 3 red lights. Answer to 2 decimal places. b)Find the probability that she hits at least 3...

A commuter must pass through five traffic lights on her way to work and will have...

A commuter must pass through five traffic lights on her way to work and will have to stop at each one that is red. She estimates the probability model for the number of red lights she hits (x), as shown below: x 0 1 2 3 4 5 p(x) 0.03 0.21 p 0.1 0.1 0.05 Find the probability that she hits at most 3 red lights. Answer to 2 decimal places. Tries 0/5 Find the probability that she hits at...

Suppose that the traffic on your way to work depends on the traffic the day before....

Suppose that the traffic on your way to work depends on the traffic the day before. There are 3 types of traffic: light, moderate, and heavy. If there is light traffic on day n, then there is a 30% chance there will be light traffic on the following day, and a 50% chance of having moderate traffic the following day. If there is moderate traffic on day n, then there is a 35% chance of having light traffic the next...

5. A driver encounters two traffic lights on the way to work each morning. Each light...

5. 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 combinations of colors is given in the following table: Second Light First Light R Y G R 0.31 0.02 0.18 Y 0.02 0.03 0.03 G 0.14 0.04 0.23 a) What is the probability that the first light is red? b) What is the probability that the second light is green? c) Find the...

A Bloomington resident commutes to work in Indiannapolis, and he encounters several traffic lights on the...

A Bloomington resident commutes to work in Indiannapolis, and he encounters several traffic lights on the way to work each day. Over a period of time, the following pattern has emerged: - Each day the first light is green - If a light is green, then the next one is always red - If he encounters a green light and then a red one, then the next will be green with probability 0.6 and red with probability .4. - If...

A single lane road is designed for a speed of 75kmph having a two-way traffic with...

A single lane road is designed for a speed of 75kmph having a two-way traffic with radius of 350m. Determine the following (use different reaction time for question i, ii & iii). Stopping Sight Distance for plain road. Stopping Sight Distance for ascending and descending gradient of 1/75. Overtaking sight distance. (take interpolated value for ‘a’) Sketch of maximum overtaking zone distance and sign posts. Setback distance for SSD (only plain road) and OSD for curve length of 150m and...

Another student must pass through 12 sets of traffic lights on his way to university each...

Another student must pass through 12 sets of traffic lights on his way to university each day. Suppose that each of the lights is green 36% of the time, yellow 5% of the time, and red 59% of the time. Suppose it is known that the traffic lights function independently. (a) What is the probability that the student encounters exactly five red lights on his way to university one day? (b) What is the probability that the student encounters at...

Yet in his understated way, Zhang is proving as radical as his predecessor. He says Alibaba...

Yet in his understated way, Zhang is proving as radical as his predecessor. He says Alibaba is uniquely positioned to pull together the online and offline worlds in groceries and beyond, and dozens 3 of his new initiatives are leading Alibaba deeper into fields including finance, health care, movies, and music. Especially in the U.S., where the company’s shares trade, these efforts have baffled some investors, who worry about overreach. In Zhang’s view, they’re a matter of survival. “Every business...

Yet in his understated way, Zhang is proving as radical as his predecessor. He says Alibaba...

Yet in his understated way, Zhang is proving as radical as his predecessor. He says Alibaba is uniquely positioned to pull together the online and offline worlds in groceries and beyond, and dozens of his new initiatives are leading Alibaba deeper into fields including finance, health care, movies, and music. Especially in the U.S., where the company’s shares trade, these efforts have baffled some investors, who worry about overreach. In Zhang’s view, they’re a matter of survival. “Every business has...

A person's blood pressure is monitored by taking 5 readings daily. The probability distribution of his...

A person's blood pressure is monitored by taking 5 readings daily. The probability distribution of his reading had a mean of 132 and a standard deviation of 3. a. Each observation behaves as a random sample. Find the mean and the standard deviation of the sampling distribution of the sample mean for the five observations each day. b. Suppose that the probability distribution of his blood pressure reading is normal. What is the shape of the sampling distribution? c. Refer...

Subjects