Week 4: Practice Problem

Problem Exercise: Probability

1. A bag of candy contains 10 red candies, 7 blue candies, 8 green candies and 5 orange ones. If a candy is taken at a random from the bag, what it the probability that it will be:

1. Red
2. Orange
3. Green or Red
4. Not Blue

1. Nine balls, each marked with a different number from 1 to 9, are placed in a bag. One ball is removed at random. What is the probability that the number on the ball is:

1. Odd
2. A multiple of 3
3. A 5
4. Nota 7

3. The owner of a restaurant serving Continental-style entrées was interested in studying ordering patterns of patrons for the Friday to Sunday weekend time period. Records were maintained that indicated the demand for dessert during the same time period. The owner decided that two other variables were to be studied along with whether a dessert was ordered: the gender of the individual and whether a beef entrée was ordered. The results were as follows:

A waiter approaches a table to take an order. What is the probability that the first customer to order at the table:

22. Orders a dessert? (Orders a Dessert) = 136/600 = 22.67%

1. Does not order a beef entrée?

1. Orders a dessert or a beef entrée?

1. Is a female and does not order a dessert?

1. Orders a dessert and a beef entrée?

1. Is a female or does not order a dessert?

1. Suppose the first person that the waiter takes the dessert order is from a female. What is the probability that she does not order dessert?

1. Suppose the first person that the waiter takes the dessert order from ordered a beef entrée. What is the probability that this person orders a dessert?

1. 60% of companies in an industrial estate own their premises, and 40% employ more than 30 people. What is the probability that a company owns its premises or employs more than 30 people?
2. The probability that it is Friday and that a student is absent is 0.03. Since there are 5 school days in a week, the probability that it is Friday is 0.2. What is the probability that a student is absent given that today is Friday?
3. The probability that a regularly scheduled flight departs on time is 0.83, the probability that it arrives on time is 0.92, and the probability that it departs and arrives on time is 0.78. Find the probability that a plane:
4. Arrives on time given that it departed on timeP (A l D) = P (A and D)/P (D) = 0.78/0.83 = 93.98%
5. Departed on time given that it has arrived on time

Solution:

7. The students in a class can be described as follows:

1. If you choose a student from the class at random and she is female, what is the probability that she is from overseas?
2. If the student is from overseas, what is the probability that the student is female?
3. A chemical plant holds a ballot for all its employees to decide whether or not to accept a new pay deal. At the ballot, 80% of the employees voted and it is known that 60% of the employees are union member. The union ascertains that 90% of the employees are either union members or voted (or both). What is the probability that an employee selected at random is a union member who voted.

9. At a concert concessionary tickets are available to those who are under 18 and those who are over 70s. It is known that 28% of the tickets are sold under 18 and 37% to the over 70s. What is the probability that an individual chosen at random has a concessionary ticket?
10. A newspaper report describing types of occupation of professional workers states that 24.6% of all workers are managerial, 55.2% of all workers are male, and 66.1% are male or managerial (or both). What percentage of the professional workers are male and managerial?

11. A trade union knows that 15% of the employees in a shoe plant are both union members and are willing to strike. Altogether 35% of the employees are union members. What is the probability that an employee who is a union member is willing to go out on strike?

Tutorial for Practice Problem