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Probability and Statistics Problems in Economics, Exams of Economics

Ashoka UniversityEconomics

A set of 15 probability and statistics problems related to various topics in economics, such as committee formation, probability of poker hands, permutations, probability of drawing balls from an urn, correlation between verbal and mathematical skills, probability of winning a math contest, probability of misdiagnosis by a doctor, probability of getting 3 aces in a card game, and probability of penalty kicks being blocked in football. The problems cover a wide range of concepts in probability and statistics, and their solutions would require a strong understanding of these topics as well as their application in an economic context. The document could be useful for students studying economics, particularly those enrolled in the eco 1400 course, as it provides practice problems and an opportunity to apply their knowledge of probability and statistics to real-world economic scenarios.

Typology: Exams

2022/2023

Uploaded on 10/02/2023

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Problem Set 1: ECO 1400
Ashwini Deshpande
September 22, 2023
Each question is worth 4 marks.
1. A committee of 5 is to be formed from 6 men and 4 women. In how many ways can it be
formed, if at least two women are included in the committee?
2. During the Second World War, gunners in RAF bombers returning from missions were
asked from which direction they were most frequently attacked by enemy fighter planes. The
majority answer was ‘from above and behind’.
Suppose you had been about to become a gunner on a bomber and had heard about this.
You might have thought ‘I’d better concentrate on the skies above and behind us’. Why might
it have been unwise to assume that this would be true of attacks on bombers in general?
3. What is the probability of getting three-of-a-kind and a pair (i.e three cards of one rank,
and two cards of another rank) in the same hand for a 5 card hand poker hand?
4. In how many ways can 18 girls and 14 boys be arranged in a line?
5. Given 1234567890, count the number of permutations possible for this, such that no ele-
ment appears on its given location in this arrangement?
6. An urn contains 5 red, 5 black and 10 white balls. If balls are drawn without replacement,
what is the probability that in the first 7 draws, at least one ball of each colour is drawn?
7. A mathematics test that includes verbal questions has been criticised on the grounds that
it gives an unfair advantage to students with high verbal ability. To check the validity of the
criticism, you test the students on separately on a verbal and mathematical skills exams. The
correlation coefficient on these two scores is close to zero. Is the criticism valid?
8. Four students (two male: A, B, and two female: C, D) submitted correct answers to a
math contest with two prizes. The contest rules specify that if more than 2 correct responses
are submitted, the winners will be selected at random from those submitting correct responses.
a) Write the set of possible outcomes for selecting two winners from the four correct responses.
b) What is the probability of each outcome?
c) What is the probability that the winners will be the same gender?
d) what is the probability that at least one winner will be female?
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Download Probability and Statistics Problems in Economics and more Exams Economics in PDF only on Docsity!

Problem Set 1: ECO 1400

Ashwini Deshpande

September 22, 2023

Each question is worth 4 marks.

  1. A committee of 5 is to be formed from 6 men and 4 women. In how many ways can it be formed, if at least two women are included in the committee?

asked from which direction they were most frequently attacked by enemy fighter planes.2. During the Second World War, gunners in RAF bombers returning from missions were The majority answer was ‘from above and behind’. Suppose you had been about to become a gunner on a bomber and had heard about this. You might have thought ‘I’d better concentrate on the skies above and behind us’. Why mightit have been unwise to assume that this would be true of attacks on bombers in general?

  1. What is the probability of getting three-of-a-kind and a pair (i.e three cards of one rank, and two cards of another rank) in the same hand for a 5 card hand poker hand?
  2. In how many ways can 18 girls and 14 boys be arranged in a line?
  3. Given 1234567890, count the number of permutations possible for this, such that no ele- ment appears on its given location in this arrangement?

what is the probability that in the first 7 draws, at least one ball of each colour is drawn?6. An urn contains 5 red, 5 black and 10 white balls. If balls are drawn without replacement,

  1. A mathematics test that includes verbal questions has been criticised on the grounds that it gives an unfair advantage to students with high verbal ability.criticism, you test the students on separately on a verbal and mathematical skills exams. The To check the validity of the correlation coefficient on these two scores is close to zero. Is the criticism valid?
  2. Four students (two male: A, B, and two female: C, D) submitted correct answers to a math contest with two prizes. The contest rules specify that if more than 2 correct responsesare submitted, the winners will be selected at random from those submitting correct responses.

a) Write the set of possible outcomes for selecting two winners from the four correct responses. b) What is the probability of each outcome? c) What is the probability that the winners will be the same gender? d) what is the probability that at least one winner will be female?

1

  1. When a doctor examines a patient, the possible outcomes are: O 1 = correct diagnosis; Ofailure); 2 = no fault diagnostic error; O O 3 = system related diagnostic error (faulty report, equipment related and cognitive errors. The associated probabilities of these outcomes are 0.85, 0.01, 0.03,^4 = cognitive diagnostic error; and^ O^5 = misdiagnosis due to a combination of system 0.04 and 0.07 respectively. a) what is the probability that a randomly selected patient is misdiagnosed? b) what is the probability that a randomly selected patient is misdiagnosed due to cognitive errors?
  2. Five players are dealt three cards each. What is the probability of a player getting 3 aces?
  3. In how many ways can a pack of 52 cards be divided among 4 players such that 3 players get 17 cards each, and one player gets 1 card?

smaller of them is strictly less than 4?12. Two numbers are selected from the set 1, 2, 3, 4, 5, 6. What is the probability that the

dents, 2 students have the same birthday? (Assume: 365 days in a year).13. The Birthday Problem: what is the probability that in the ECO 1400 class of 40 stu-

  1. A drawer has five blue socks and four black socks. A woman takes two socks out at random. What is the probability that they match?
  2. Penalty kicks in football: Consider the following events. L = the event that the goalkeeper jumps to the left C = the event that the goalkeeper stays in the centreR = the event that the goalkeeper jumps to the right B = the event that the penalty kick gets blocked.

P(B|R) =0.126; P(L) = 0.493; P(C) = 0.063; P(R) = 0.444Based on an analysis of 286 penalty kicks, we know that P (B|L) = 0.142 ; P (B|C) = 0.333; What proportion of kicks were blocked?