Question 1

The table below gives the probability of workers in a factory being late (in days per week). Calculate the expected value from this data.

Accepted Answer

A)  0.53 
B)  0.58 
C)  0.63 
D)  0.68 
A)  0.53 
B)  0.58 
C)  0.63 
D)  0.68 C

Question 2

A law firm in Sana'a employs 8 lawyers, 6 have expertise in employment law and 5 have expertise in company law, 1 is expert in neither area. If you meet one of these lawyers randomly, what is the probability that they are an expert in company law and not employment law?

Accepted Answer

A)  0.5 
B)  0.375 
C)  0.25 
D)  0.125 
A)  0.5 
B)  0.375 
C)  0.25 
D)  0.125 D

Question 3

You estimate that the chance of new product being successful is 0.8 - a marketing analyst (who is correct 65% of the time) gives a favourable opinion of your product. What should you revise your estimation of success to (as a percentage, 0 decimal places)?

Accepted Answer

A)  82% 
B)  84% 
C)  86% 
D)  88% 
A)  82% 
B)  84% 
C)  86% 
D)  88% D

Question 4

The management of a parcel delivery firm in Accra, Ghana know that the chances of a parcel being delivered on time are 0.6, 0.85 or 0.7 depending on whether it goes on van A, B or C respectively. The chance of being on van A is 0.4 and the chance of being on van B is 0.35. What is the overall probability that a parcel will be delivered on time (3 decimal places)?

Accepted Answer

A)  0.634 
B)  0.659 
C)  0.683 
D)  0.713 
A)  0.634 
B)  0.659 
C)  0.683 
D)  0.713

Question 5

A factory making two types of computer chip mixes up two small batches of new chips. A box contains 50 chips, 30 are type A and 20 type B. If you take two chips out at random, what are the chances they are both type B (3 decimal places)?

Accepted Answer

A)  0.135 
B)  0.145 
C)  0.155 
D)  0.165 
A)  0.135 
B)  0.145 
C)  0.155 
D)  0.165

Question 6

A motorcycle showroom sells 80 red motorcycles each month; it sells 50 125cc bikes, 30 of which are red. What is the chance of a motorbike being 125cc if you know that it is red?

Accepted Answer

A)  35.5% 
B)  36.5% 
C)  37.5% 
D)  38.5% 
A)  35.5% 
B)  36.5% 
C)  37.5% 
D)  38.5%

Question 7

In Istanbul it rains on 25% of days. A small retailer knows that on rainy days her profits are usually low (Pr(L)=0.7) but when it is not rainy she is much more likely to make good profits (Pr(L)=0.2). On average, what are the chances that she makes a good profit on any given day (give answer as percentage, 1 decimal place)?

Accepted Answer

A)  32.5% 
B)  35.0% 
C)  37.5% 
D)  40.0% 
A)  32.5% 
B)  35.0% 
C)  37.5% 
D)  40.0%

Question 8

A factory owner in Kampala, Uganda knows that each mistake on a particular machine costs 200,000 Ugandan Schillings (UGX). The probability of no mistakes on a particular day is 0.40 and 2 mistakes occur 10% of the time, 3 mistakes happen on only 1 in 20 occasions. The rest of the time there is 1 mistake. What is the expected cost of mistakes each day?

Accepted Answer

A)  UGX 160,000 
B)  UGX 180,000 
C)  UGX 200,000 
D)  UGX 220,000 
A)  UGX 160,000 
B)  UGX 180,000 
C)  UGX 200,000 
D)  UGX 220,000

Question 9

What is the BEST definition of the expected value?

Accepted Answer

A)  The most likely value for a variable to take 
B)  The arithmetic mean of a given set of values 
C)  The median of a given set of values 
D)  The sum total of all values in a given set of data 
A)  The most likely value for a variable to take 
B)  The arithmetic mean of a given set of values 
C)  The median of a given set of values 
D)  The sum total of all values in a given set of data

Exam 31: Conditional Probability and Expectation

The table below gives the probability of workers in a factory being late (in days per week). Calculate the expected value from this data.

A law firm in Sana'a employs 8 lawyers, 6 have expertise in employment law and 5 have expertise in company law, 1 is expert in neither area. If you meet one of these lawyers randomly, what is the probability that they are an expert in company law and not employment law?

You estimate that the chance of new product being successful is 0.8 - a marketing analyst (who is correct 65% of the time) gives a favourable opinion of your product. What should you revise your estimation of success to (as a percentage, 0 decimal places)?

A factory making two types of computer chip mixes up two small batches of new chips. A box contains 50 chips, 30 are type A and 20 type B. If you take two chips out at random, what are the chances they are both type B (3 decimal places)?

A motorcycle showroom sells 80 red motorcycles each month; it sells 50 125cc bikes, 30 of which are red. What is the chance of a motorbike being 125cc if you know that it is red?

What is the BEST definition of the expected value?

Introduction to Business Mathematics and Statistics

Sampling and Data Collection

Data and Their Accuracy

Frequency Distributions and Charts

General Charts and Graphs

Arithmetic Mean

Median

Mode and Other Measures of Location

Measures of Dispersion and Skewness

Standard Deviation

Quantiles and the Quartile Deviation

Linear Functions and Graphs

Regression Techniques

Correlation Techniques

Time Series Model

Time Series Trend

Seasonal Variation and Forecasting

Index Relatives

Composite Index Numbers

Special Published Indices

Interest and Depreciation

Present Value and Investment Appraisal

Annuities

Functions and Graphs

Linear Equations

Quadratic and Cubic Equations

Differentiation and Integration

Cost, Revenue and Profit Functions

Set Theory and Enumeration

Introduction to Probability

Combinations and Permutations

Binomial and Poisson Distributions

Normal Distribution

Linear Inequalities

Matrices

Inventory Control

Network Planning and Analysis

Filters