PROBABILITY PRACTICE

(With results)
1. With the experiment of rolling a die and flipping a coin at the same time, determine: a) the space
sample, b) an experimental result, c) at least two events d) the probability of
occurrence of events.
2. Suppose the throwing of three coins through a tree diagram determine: a)
sample space, b) the probability that at least two heads exist, c) the probability that
at most there are two faces d) the probability of the existence of a single shield.
Respuestas: b) 0,5 c) 7/8 d) 3/8
3. Do the previous exercises meet the basic requirements for assignment?
probabilities?, Why?. Explain
Answer: if they meet the basic conditions of probability.
4. Suppose an experiment has four equally probable outcomes: E1, E2, E3, E4. Assign
probabilities for each one and demonstrate that the basic requirements are met for
assignment of probabilities. What method do I use?

Answer: each result has a 0.25 probability and satisfies both conditions because none
exceeds one or is negative and the sum of the four results equals one. The method that is
The method is employed. The classical method is used.

5. According to the theory of probability allocation methods the following

experiments, which method would they correspond to?
Russian roulette. (classic method)
b) The possibility of it raining today (subjective method)
c) A production unit will be defective (relative frequency)
d) A game of cacho (classic)

6. An experiment with three outcomes was repeated 50 times, and it was observed that E1 occurred 20 times, E2 13 times.
y E3 17. Assign probabilities to the results What method do I use?

20/50 13/50 17/50 the relative frequency method is used.

A graduate from the school of business and commerce has assigned subjectively
the following probabilities for the three outcomes of an experiment: P ( 1 )= 0.24, P(E2) = 0.24
y P(E3) = 0.48. Is this a valid probability assignment? Explain your answer in detail.

Answer: It is not valid because the sum of the probabilities does not equal one, it only reaches 0.96.
8. During the last two league football matches, the coin toss came up heads every time.
the times. The captain of the Aurora team who must now make the decision to choose an option,
he thinks that asking for a shield this time will increase the probability of winning the toss. Is it in the ...
Is it true or is it wrong? Use the method that you think is best to support your answer.

Response: this is an experiment to deal with the classic method because the result is
equiprobable, additionally each experiment is independent, so the result does not
It will depend on previous results, the captain of Aurora is mistaken.

9. Sales in the appliance store according to the record of a complete month have been
“poor” for 6 days, “low” for 9 days, “mediocre” for 6 days, “good” for 2 days and
"excellent" 7 days. a) What is the probability of each of these events? b) Do they meet the
basic conditions of probability? C) What is the probability that today's sales
Are they at least mediocre? D) What is the probability that they are less than good?
E) What is the probability that they are more than good?

Answers:

a)

x frec probability
Very bad 6 0.2
low 9 0.3
mediocre 6 0.2
good 2 0.067
excellent 7 0.233
total 30 1

b) They meet the basic conditions of probability. 0.5 0.7

In the entrance exam, students have been classified as passed (A) and failed.
Economics
Commercial (IC), Accounting (C) and Financial Engineering (IF). Create a contingency table.
the relationship between the variables is identified.

Ing. Eng. Accounting

Commercial Administration Financial Economics publish Total
approved
failed
Total S
 11. Given the conditions of exercise 10, identify the events that are: a) mutually
a) mutually exclusive, b) collectively exhaustive, c) complementary. d) if 20 out of the 200 students
they have rejected your application to the commercial engineering program. What is the
probability of not choosing them if a random selection is made?

Answers:

a) Passing a subject excludes the possibility of failing it at the same time

b) All the attributes of the variable 'career' are collectively exhaustive among themselves.
c) The approved attribute is complementary to the failed one.
d) P(R and IC) complement = 180/200
12. The magazine nueva economía launched a ranking of the 300 largest companies in Bolivia, of these
75 companies have headquarters in La Paz, 97 in Santa Cruz, 62 in Cochabamba, 20 in
Oruro, 15 in Tarija and the rest are in the other departments of the country. Assume that you
Choose one of the 300 companies from the ranking. What are the odds of the following?
eventos?: a) Sea (L) la probabilidad de que la empresa se encuentre en La Paz, calcule P(L). b) Sea
(S) the probability of a venue in Santa Cruz, determine the probability of (S) C) Let (C) be
probability of Cochabamba determine the probability that the venue is not this city. d)
What is the probability that the company is not in any of the departments?
mentioned?

a) P(L) = 0.25 b) P(S) = 0,32 c) P(C) = 0,79 d) P (Otro) = 0,10

13. Data was collected from 500 professionals in the business and commercial field, regarding the
business growth prospects in the management 2012. The consulted professionals
They work in different areas of the public and private sector and expressed their opinion on three levels.
Unfortunately, part of the information was lost in the process. Complete the following
table, and create a probability table.

Business development
Stable Professionals Total
Academia (A) 125 100
Industry (I) 35 110
Government (G) 25 40 65
Total 200

14. Based on the probability table, determine the following events.

a)P(A translatedText
b) P(G C) c) P(I E) ( A C) d) P(S A)

e) P(G C) f )P(I C) Cg)P(I E) h)P(A/E) P(E/A)

c
j) P(I E) (A k)P(A/C)C
 15. The police force is made up of 1200 officers, of which 960 are men and 240 are women.
Women. In recent years, 324 officers have been promoted, and the details are in the table.

Men
Ascended (A) 288 36 324
Not promoted (N) 672 204 876
Totals 960 240 1200

In this police district, a report has been filed for ongoing sexual discrimination based on the assumption
that male officers are more favored in promotions. You as a statistician,
determine the truthfulness of these statements by calculating the probability of selecting an officer
for the promotion since this is a man and on the other hand the selection of an officer for the promotion
Given that she is a woman. Do you think there is discrimination?

Men Totals

Ascended (A) 0.24 0.03 0.27

Not promoted (N) 0.56 0.17 0.73

Totals 0.8 0.2 1

Response: P(A/H)=0.3 P(A/M) = 0.15 Men are more likely to be

ascended by their gender.

16. Out of 200 professionals, 115 are Administrators and the rest are Business Engineers.
The last 25 are unemployed, while 80 managers have jobs. What is the
probability of the following relationships?

unemployed or engineer
b) Administrator or engineer
c) He/She is not unemployed
d) He is not an employee manager.
e) It is known that he is an administrator. What is the probability of this employee?
f) He is unemployed. What is the probability that he is an engineer?

Respuestas: a) 0,6 b)1 c) 0,7 d) 0,6 e) 0,6956 f) 0,4166

17. A stockbroker knows from past experience that the probability of a client
The likelihood of the customer buying a government bond is 65% if
he/she already has shares, it is 35%.
 a) What is the probability that the customer has both?
b) Are B and S independent? Explain.

0.23
18. A lender has two debtors whose deadlines expire today (we assume independence.
of the events), it is known from experience that debtor A pays on time 45% of the
opportunities as far as debtor B is 70%. What is the probability that the lender
Wait for the following events?

no debtor pays.
Only one does it
Both pay
At least one shows up.

Respuesta: a) 0,165 b) 0,52 c) 0,315 0.835

19. When rolling two dice, what is the probability of getting

a) A total of 7 points in the first throw, followed by 11 in the second?

a total of 21 points in the first two combined throws?
c) A total of 6 in the first three combined rolls?

Respuesta: a) 0,009259 b) 6/1269 c) 3/1269

20. The following Venn diagrams indicate the number of outcomes of an experiment
corresponding to each event and the number of results that do not correspond to any event.
Taking into account these diagrams, provide the requested probabilities:

Respuestas: P(A)= 0,18 P(B)=0,12 P(A o B) = 0,30

21. The probability that a student fails costs is 0.8, that they pass Statistics is
0.5 and the probability of failing in markets is 0.4. (One event does not influence the occurrence of the other)
Determine the probability that:
a) Approve a subject.
b) Approve at least one subject.
c) Approve at most one subject.
d) Fail the three subjects.
a) P( x=1) = 0.44 b) P(x≥1)= P (x=1) + P(x=2) + P(x=3) = 0.44 + 0.34 + 0.06 = 0.84
c) P(x≤1) = P(x=0) + P(x=1) = 0.16 + 0.44 = 0.6 d) failing three is the same as passing none
then P(x=0) = 0.16

COSTS MARKET STATISTICS

APPROVE 0.2 0.5 0.6
to fail 0.8 0.5 0.4

I approve 0 0.16
I approve 1 0.04 0.16 0.24 0.44
I approve 2 0.04 0.06 0.24 0.34
I approve 3 0.06
total 1

22. A study has determined that 15% of executive positions in large companies...
companies are occupied by women, it has also been determined that four percent of the
male executives have a doctorate in their field while 20% of women do.
These positions require this degree. A) A person is selected from the sample. What is
the probability of being a doctor? B) A professional with a doctoral degree is randomly selected.
What is the probability of being a woman?
0.064 0.47 0.53

23. A local bank is reviewing its credit card policy with the aim of canceling some of
In the past, approximately 5% of cardholders have stopped paying without the
bank has been able to recover the debt. Consequently, management has established that there is a
a priori probability of 0.05 that a cardholder will incur in delinquent debt. Furthermore, the
the bank has seen that the probability of a regular customer falling behind on one or more payments
The monthly rate is 0.20. Naturally, the probability of delay in one or more payments for the
Clients that incur in overdue accounts is 1. a) If a client is late on a monthly payment,
calculate the posterior probability that the client will incur in default. B) To the bank it
I would like to cancel a customer's credit line if the likelihood of them defaulting is high.
If the overdue amount is greater than 0.20, should a line be canceled if a customer is late on a monthly payment?
Why yes or why not?
Answers:
a) The probability that a customer will fall into default given that they are delayed in payment.
monthly is 20.83%.
b) Since the probability of incurring in overdue portfolio exceeds 20%, the line should be canceled.
credits.

24. A study indicates that of all the people who dare to start their own business, the
20% I requested a loan to start it. Of the people who requested the loan, 70% had
 success in entrepreneurship, while of the people who did not opt for the loan, a
65% was successful. A person who failed in business was selected:

a) What is the probability that they have applied for credit?

b) What is the probability that no credit has been requested?

0.176 b) 0.824

25. The credit department of a shopping center reported that 30% of sales are paid with
cash or with a check; 30% is paid with a credit card and 40% with a debit card. Twenty
percent of purchases with cash or check, 90% of purchases with a credit card and
60% of debit card purchases are for more than $50. Mrs. Tina Tramon has just
buy a new dress that cost him $120. What is the probability that he paid in
cash or with a check?
Response: the probability is 0.105.

26. On the same day, the professional basketball team plays at home and the football team
the same city plays as a visitor. A professional basketball team has a
a probability of 0.641 of winning the home game and a professional soccer team has a
probability of 0.462 of winning as a visitor. Historically, when both teams play
On the same day, the probability that the main headline refers to the basketball game is 66%.
and that of the football game of 34%. Suppose that the morning of a day with this type of encounters
With the heading of the sports section is 'We Won!'.

a) What is the probability that it does not refer to the football team?
b) What is the probability that it does not refer to the basketball team?

a) 0.729 0.271

27. Out of the 10 executives, 3 will be selected to serve as president, vice president,
and treasurer. How many selections are possible?
Response: 720 possible selections.

28. Of the 12 employees of Megaoutled Travel, 7 have had special training. If 5 employees
They are going to be sent to Brazil. What is the probability that 3 are among those who have had
special training?
Response: 0.44

29. Of the 15 members of the board of directors of a large company. How many committees of 5 members?
Can they be selected if the order matters?
Response: 360,360 selections.
30. Your company is testing a new product and has been able to determine that 20% of the
consumers express their dissatisfaction with it, of the satisfied consumers, 60%
They make more orders, obviously in the case of people who were not pleased with the product.
none placed a new order. People who have not made more than one are being tracked.
order, what is the probability that they were satisfied with the product the only time that
Did they consume it?
0.615