Deck 31: Conditional Probability and Expectation

Question 1

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)?

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

Answer 1

32.5%

Question 2

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)?

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

Answer 2

0.659

Question 3

What is the BEST definition of the expected value?

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

Answer 3

The arithmetic mean of a given set of values

Question 4

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?

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

Question 5

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

Question 6

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) 0.135
B) 0.145
C) 0.155
D) 0.165

Question 7

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?

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

Question 8

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?

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

Question 9

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) 0.53
B) 0.58
C) 0.63
D) 0.68