Q1. Consider the following out come for experiment:
Outcome (x)
Probability p(x)
1
0.2
2
0.25
3
0.15
4
0.10
5
0.30
a. Let event A consist of the outcomes 2, 4, and 5 and event B consist of out
come 4 and 5. Find the probability the either A or B occurs
b. Find the mean and standard deviation of the outcome of the experiment.
Q2: A recent survey in a city revealed that 60% of the vehicles traveling on
highways, where speed limits at 70 miles per hour, were exceeding the limit.
Suppose you randomly checked the speeds of 3 vehicles traveling on a highway
where the speed limit is 70 miles per hour
1. list the sample space of possible responses indicate a car speeding or not.
2. What is the probability that first car was not speeding but the next two were?
3. Find the probability that one of the three cars was speeding.
4. IF you know that more than one car was speeding, find the probability that
All of the three cars were speeding?
Q3: Let X be a binomially distributed random variable with mean equal to 4 and
variance equal to 4/3.
1. Find the distribution of the random variable X
2. From (a) show that the mean equal to 4
3. From parts (a) and (b), show that the variance equal to 4/3.
Q4: The traffic light at Main Street and Broadway is green, red or yellow for Main
Street. Traffic with the following probabilities: P(green) = 0.7, P( red) = 0.25 and
P(yellow) = 0.05. Find the probability that at least 3 out of 5 cars on the Main
Street get a green light at the intersection.
Q5: Widgets are produced in lots of forty. If a lot contains six defective widgets,
what is the chance that a sample of five will contain two or more defective
widgets?
Q6: Mohammad is applying for 8 jobs and believes that he has in each case the
same probability of .42 getting an offer.
1. What is the probability of getting at most three offers?
2. What is the probability of getting no offers?
3. What is the mean and standard deviation for job offers?
Q7: Two identical bags are filled with colored balls. The first bag has 70 green and
30 red balls; call this G. the second bag contains 30 green and 70 red balls; call
this R. The balls are identical except for color. Choose one of the bags, and set the
other aside. A random sample of 12 balls are chosen without replacement. Given
that there are 8 green and 4 red balls in the sample, what is the probability that the
bag is G
Q8: The number of accidents on a city is in average 10 accidents per a day, find
the probabilities that there will be:
a) exactly 8 accidents in the coming day,
b) fewer than 5 accidents per a given day,
c) more than 3 accidents in first 12 hours in the coming day.
d) What is the mean and variance of the number of accidents per two days?
Q9 The number of passengers arriving at a particular bus stop is Poisson
distributed with a mean rate of 1.2 passengers per minute.
1. Calculate the probability that more than 4 passengers arrive in the next 3
minutes.
2. Calculate the expected number of passenger arrivals in a 5 minutes interval.
Also, calculate the standard deviation of the number of arrivals in 5 minutes.
3. If we are told that 15 passengers have arrived between 7;00 A.M and 7:10
A.M, calculate the probability that 10 out if 15 passengers arrived in the last
5 minutes ( i.e., between 7:05 A.M and 7:10 A.M)