Assignment Q:- 1. An experiment has four equally likely outcomes: E1, E2, E3, and E4. a. What is the probability that E2 occurs? b. What is the

Assignment

Q:- 1. An experiment has four equally likely outcomes: E1, E2, E3, and E4.

a. What is the probability that E2 occurs?

b. What is the probability that any two of the outcomes occur (e.g., E1 or E3)?

c. What is the probability that any three of the outcomes occur (e.g., E1 or E2 or E4)?

Q:- 2. Consider the experiment of selecting a playing card from a deck of 52 playing cards. Each card corresponds to a sample point with a 1/52 probability.

a. List the sample points in the event an ace is selected.

b. List the sample points in the event a club is selected.

c. List the sample points in the event a face card (jack, queen, or king) is selected.

d. Find the probabilities associated with each of the events in parts (a), (b), and (c).

Q:- 3. An integer is chosen at random from the first 100 positive integers. Find the probability that it is divisible by:

1. 8 or 12 (b) 16 and 20

Q:- 4. A class contains 10 men and 20 women of which half of the men and half of the women have brown eyes. Find the probability that a person chosen at random is a man or has brown eyes?

Q:- 5. President of a commercial bank interested to appoint manger to a newly open branch from his personal staff by selecting a person at random. The details of his personal is given as under:

What are the chances that the staff the staff member selected for the post of manger will be:

1. A Male (b) Graduate (c) Post Graduate Female (d) Male or Intermediate

(e) If selected person is Matric, then Female (f) If Selected person is Male than Graduate

Q:- 6. A bag contains 10 light bulbs out of which 3 are defective. If two bulbs are selected at random from the bag, what is the probability that both are not defective?

Q:- 7. Consider the experiment of rolling a pair of dice. Suppose that we are interested in the sum of the face values showing on the dice.

a. How many sample points are possible?

b. List the sample points.

c. What is the probability of obtaining a value of 7?

d. What is the probability of obtaining a value of 9 or greater?

e. Because each roll has six possible even values (2, 4, 6, 8, 10, and 12) and only five possible odd values (3, 5, 7, 9, and 11), the dice should show even values more often than odd values. Do you agree with this statement? Explain.

f. What method did you use to assign the probabilities requested?

Q:- 8. Suppose that a manager of a large apartment complex provides the following subjective probability estimates about the number of vacancies that will exist next month.Provide the probability of each of the following events.

a. No vacancies

b. At least four vacancies

c. Two or fewer vacancies

Q:- 9. Asurvey of 50 students at Tarpon Springs College about the number of extracurricular activities resulted in the data shown.

a. Let A be the event that a student participates in at least 1 activity. Find P(A).

b. Let B be the event that a student participates in 3 or more activities. Find P(B).

c. What is the probability that a student participates in exactly 2 activities?

Q:- 10. Suppose that we have a sample space with five equally likely experimental outcomes: E1,E2, E3, E4, E5.

Let

A= {E1, E2}

B ={E3, E4}

C ={E2, E3, E5}

a. Find P(A), P(B), and P(C).

b. Find P(A U B). Are A and B mutually exclusive?

c.. Find P(B U C).

Q:- 11. On a single toss of a pair of fair dice, what is the probability that a sum seven happens or both dice show a number less than 4?

Q:- 12. In a group of 20 adults, 4 out 7 women and 2 out of 13 men wear glasses. What is the probability that a person chosen at random from the group is a woman or someone who wear glasses?