Statistics in Business
Sections 4 and 5
Class 03 Assignment Answers
1. George reluctantly agreed to feed your fish over the holiday break. You think there is a 40% chance
George will forget. If he forgets, the fish will almost certainly die (probability 0.90). If he does feed the
fish, it will almost certainly survive (probability 0.95). Upon return from break, your fish is dead. Did
George feed it?
1. For convenience let’s count what we expect to happen in 100 trials.
Fish Live
George Feeds
George Forgets
Fish Die
57
4
61
So P(George feeds given Fish Died) = 3/39 =
P(George forgot given the fish died) = 36/39 =
We can also use a formula to answer this question.
Total
3
36
39
60
40
100
0.076923
0.923077
2. (EMBS problem 41, page 190) A consulting firm submitted a bid for a large research project. The firm’s
management initially judged they had a 50/50 chance of getting the project. However, the agency to
which the bid was submitted subsequently requested additional information on the bid. Past experience
indicates that for 75% of the successful bids and 40% of the unsuccessful bids the agency requested
additional information. Now that the agency has requested additional information, what are the
chances the firm’s bid will be successful?
2. For convenience, let's count what to expect to happen in 100 trials
Fail
Success
Total
20
37.5
30
12.5
50
50
request for info
no request
So P(Success given request for info) = 37.5/57.5 =
57.5
42.5
100
0.652174
3. (EMBS problem 37, page 184) Visa Card USA studied how frequently young consumers (ages 18 to 24)
use plastic in making purchases. (AP, January 16, 2006). The results of the study provided the following
probabilities:


The probability that a consumer uses plastic when making a purchase is 0.37
Given that the consumer uses plastic, there is a 0.19 probability the consumer is young (18 to 24)
and a 0.81 probability the consumer is not young.
About 14% of US purchases are made by young consumers (18 to 24). Given that the consumer is young,
what is the probability that consumer used plastic? Given that the consumer is not young, what is the
probability that consumer used plastic? Are age and using plastic independent events?
3. For convenience, let's count what we expect to happen in 1,000 purchases.
not
Young
not
Plastic
69.7
560.3
630
Total
70.3
299.7
370
So P(plastic given young) = 70.3/140 =
P(plastic given not young) = 299.7/850 =
Young and plastic are NOT independent because the probability
of using plastic is higher (than 37%) given the consumer is young.
140
860
1000
0.502143
0.348488
4. After a semester of practice, Bo claims to be able to flip heads. What would be the more challenging
test of Bo’s supposed skill……requiring at least 8 heads in 10 flips or 60 in 100?
4. Assume he cannot "flip head" and that the number of heads
will follow the binomial distribution with p=0.5.
P(8 or more) = 1 - P(7 or fewer) = 1 - BINOMDIST(7,10,.5,true)
=
0.054688
P(60 or more in 100) = 1 - BINOMDIST(59,100,.5,true)
=
0.028444
So flipping at least 60 in 100 is more difficult than 8 or more in 10.
5. Tim Abromaitis, a 78% free throw shooter, will attempt three free throws late in a close game. What
are the chances he’ll make at least two of the three attempts? State any assumption you need to make
to answer this question.
5. Assume free throw outcomes are independent and 0.78 is based
on enough data so that it is a probability. The number of successes
in three trials will be binomially distributed.
P(2 or more) = 1- P(1 or fewer)
= 1 - BINOMDIST(1,3,.78,true)
=10.123904
=
0.876096