Question

1)Find the permutation and combination of the letters a, b, c, d taking 2 at a time.

Verify your answers with the permutation & combination formula.2)

2.An urn contains 10 marbles. 3 blues, 4 yellow and 3 red marbles. 6 marbles is selected at random. Find the probability of picking 1 blue, 3 yellow marbles and 2 red ones.

3) A computer operator has to issue passwords made up of a letter followed by two digits. How many passwords are possible? Give two random passwords

4) In how many ways can you mark a 5-question test True / False? Give a random selection

5) A recent U.S survey shows that, the probability of living in California is 12%, the probability

of being Hispanic is 11% and the probability of being Hispanic and living in California is 4%.

Let H represents the events of “Being Hispanic” and L for living in CA. Evaluate i) P(H/L), ii)P(H U L)

6) A single card is picked at random. Find the probability of picking a red card or a 10.

7) a)Define mutually vs not mutually exclusive events give an example of two events that are mutually exclusive and two that are not.

b)Define independent events and give an example of an independent event and a dependent one.

c)Define independent events and give an example of an independent event and a dependent one.

8) a)A coin is tossed three times, use a tree diagram to construct all the possible outcomes.

8b)The odds-maker give the Yankees a 10 to 1 shot of winning the 2020 World Series.

What is the probability that the Yankees will win the 2020 World Series?

9)In Spring valley, NY about 56% of days in a year are cloudy. Find the mean,
variance and standard deviation for the number of cloudy days during the month of June

10) The probability that Yankees will 2020 world series is 20%.

Find the odds in favor that they will in fact win the 2020 world series? .20 to 1-.20 which reduces to 1 to 4 odds.

11. A sample task was given to 150 elementary school children.

The following table includes the times in minute it takes to complete the task.

minutes	# of kids
1 2 3 4 5	24 33 42 30 21 ----------- Total= 150

a) Construct a probability distribution for the random variable x

b) Graph the distribution using a histogram (Times in minutes VS probability)

c) Verify that the probability is in fact a probability distribution.

d) Find the mean, the variance and the standard deviation

12) The table shows the number of male and female students enrolled in nursing at University of Oklahoma Health Sciences center for a recent semester.

A student is selected at random. Find the probability of each event.

Nursing Majors     Non Nursing Majors     Total

Males                 94                    1104                             1198

Females             725                    1682                           2407

Total                  819                    2786                            3605

Calculate the probability of a) choosing a male or a nursing major is

b)      The student is a female or not a nursing major. c)The student is a female given that nursing major d) Calculate P(M U F), P( M n F)

15)The probability that a person in the United States has type A+ blood is 31%. Three people in the United States are selected at random. Find the probability that

a) All three has blood type A+   b) None of the three has blood type A+

c) At least one of the three has blood type A+. d)Which of the events can be considered unusual? Explain

Answer 1