Chapter 4 Practice Worksheet

Chapter 4 Practice Worksheet

Chapter 4 Practice Worksheet

  1. A couple plans to have three kids. Find the probability of:

a)Getting at least one girl.

b)All boys

c)All girls

d)Two boys or two girls

  1. The probabilities that a student will get passing grades in math, English, or both are P(M) = 0.70, P(E) = 0.80, and P(M and E) = 0.56. Check if M and E are independent.
  1. The probabilities that it will rain on Rosh Hashanah, Ramadan, or both are

P(R.H.) = 0.60, P(Ram) = 0.60, P(R.H. and Ram) = 0.42. Check if Rosh Hashanah and Ramadan are independent.

  1. The local Chamber of Commerce conducted a survey of one thousand randomly

selected shoppers at a mall. For all shoppers, “gender of shopper,” and “items

shopping for” was recorded. The data collected is summarized in the following

table:

If the shopper is selected at random from this mall,

a)What is the probability that the shopper is a female?

b)What is the probability that the shopper is shopping for shoes?

c)What is the probability that the shopper is a female shopping for shoes?

d)What is the probability that the shopper is shopping for shoes given that the

shopper is a female?

e)Are the events “female” and “shopping for shoes” disjoint?

f)Are the events “female” and shopping for shoes” independent?

  1. A VCR Manufacturer gets 70% of its parts from factory F1 and the rest from Factory F2. 3% of the output from F1 are defective while 2% of the output from F2 are defective.

a)Find the probability that a received part is defective.

b)If a randomly chosen part is defective, what is the probability it came from Factory 1?

c)If a randomly chosen part is defective, what is the probability it came from Factory 2?

  1. A medical examiner must randomly select one of the two RH types (+,-) and one of the four blood groups (A, O, B, AB). What the the total number of possible outcomes?
  1. Suppose a salesperson must visit 3 cities A, B, and C. How many routes are possible?
  1. We only have time to visit 4 of the state capitols. What are the number of possible routes?
  1. How many ways can we arrange the letters DDDDRRRRR?
  1. You roll the dice.

a)How many outcomes are there?

b)Find P(2), P(4), P(12) and P(7 or 11).

  1. There are 80 applicants seeking to obtain a fast-food franchise. Some of these persons are college graduates and some are not. Some have prior experience in the food service industry and some do not. The exact breakdown is:

College Grads / NotCollege Grads
Prior Food Experience / 24 / 36
No Prior Food Experience / 12 / 8

If the order in which the applicants are processed is random, G is the event that the first applicant processed is a college graduate, and E is the event that the first applicant processed has prior food service experience, determine each of the following probabilities:

a)P(G)

b)P(compliment of E)

c)P(E and G)

d)P(compliment of E and compliment of G)

e)P(E given G)

f)P(compliment of G given compliment of E)

g)P(compliment of E given compliment of G)

h)P(E or G)

  1. The probabilities are 0.45, 0.36, and 0.18 that a person traveling in the northeastern US will visit Boston, Providence, or both.

a)Find the probability that a traveller visiting Boston will also visit Providence.

b)Find the probability that a traveller visiting Providence will also visit Boston.

  1. In Statistics class there are 18 juniors and 10 seniors; 6 of the seniors are females and 12 of the juniors are males. If a student is selected at random, find the probability of selecting (hint: draw a two-way table):

a)A junior or female

b)A senior or female

c)A junior or a senior

  1. If the Mavericks beat school A 9 times but school A beat the Mavericks twice, what are the odds for the Mavericks?
  1. There are ten people in a mile race. How many possibilities are there for places 1, 2, and 3?
  1. There is a group of ten people that a committee of 4 needs to be selected from. How many possibilities are there?
  1. Suppose you wish to randomly sample five households from a population of 100,000 households. How many different samples can be selected?
  1. How many samples of four courses can you select from a list of 25 courses in a university catalogue?
  1. Flying into New York from a certain city, you can choose one of three airlines and can travel either first class or economy. How many travel options do you have?
  1. A salesperson living in city A wishes to visit four cities, B, C, D, and E. If the cities are all connected by airlines, how many different travel plans could be constructed to visit each city exactly once and then return home?
  1. Hospital records show that 12% of all patients are admitted for surgical treatment, 16% are admitted for obstetrics, and 2% receive both obstetrics and surgical treatment. If a new patient is admitted, what is the probability that the patient will be admitted either for surgery, obstetrics, or both?
  1. For a single die, let A = {Toss an even number} and B = {Toss a number less than or equal to 3}.

a)Describe the Union (“or”) of A and B.

b)Describe the Intersection (“and”) of A and B.

c)Calculate P(A or B) and P(A and B).

d)Draw the Venn Diagram.

  1. Two companies offer overnight shipping that is supposed to arrive by 10 a.m. Your company ships 30% of its packages with shipping service 1 and 70% with shipping service 2. Shipping service 1 fails to meet the 10:00 a.m. deadline 10% of the time and shipping service 2 fails to meet it 8% of the time.
  2. Draw a tree diagram
  1. If a customer is expecting a package and it is late, which of the shipping services is the more likely to have been used?
  1. 70% of people buy Brand 1 DVD player. 30% buy brand 2. Of those who buy a DVD player, 20% of those who buy Brand 1 also get the extended warranty and 40% of those who buy brand 2 get it.
  1. Draw a tree diagram
  1. Of those who bought a DVD player, what is the probability

they got brand 1 and the extended warranty?

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