in an organization, there are total 28 employees are enrolled out of which 12 are male employees and 16 are female employees. one of them is called out by an enrolled number, what is the probability that the one called is a female employee?

get in an organization, there are total 28 employees are enrolled out of which 12 are male employees and 16 are female employees. one of them is called out by an enrolled number, what is the probability that the one called is a female employee? from screen.

40 Questions on Probability for data science

40 questions on probability to test your understanding of Probability for data science. Concepts include counting, conditional probability & Bayes Theorem

Dishashree26 — April 10, 2017

Beginner Business Analytics Career Interviews Skilltest Statistics

Introduction

Probability forms the backbone of many important data science concepts from inferential statistics to Bayesian networks. It would not be wrong to say that the journey of mastering statistics begins with probability. This skilltest was conducted to help you identify your skill level in probability.

A total of 1249 people registered for this skill test. The test was designed to test the conceptual knowledge of probability. If you are one of those who missed out on this skill test, here are the questions and solutions. You missed on the real time test, but can read this article to find out how you could have answered correctly.

Here are the leaderboard ranking for all the participants.

Are you preparing for your next data science interview? Then look no further! Check out the comprehensive ‘Ace Data Science Interviews‘ course which encompasses hundreds of questions like these along with plenty of videos, support and resources. And if you’re looking to brush up your probability sills even more, we have covered it comprehensively in the ‘Introduction to Data Science‘ course!

 

Overall Scores

Below are the distribution scores, they will help you evaluate your performance.

You can access the final scores here. More than 300 people participated in the skill test and the highest score obtained was 38. Here are a few statistics about the distribution.

Mean Score: 19.56 Median Score: 20 Mode Score: 15

This was also the first test where some one scored as high as 38! The community is getting serious about DataFest

 

Useful Resources

Basics of Probability for Data Science explained with examples

Introduction to Conditional Probability and Bayes theorem for data science professionals

 

1) Let A and B be events on the same sample space, with P (A) = 0.6 and P (B) = 0.7. Can these two events be disjoint?

A) Yes B) No Solution: (B)

These two events cannot be disjoint because P(A)+P(B) >1.

P(AꓴB) = P(A)+P(B)-P(AꓵB).

An event is disjoint if P(AꓵB) = 0. If A and B are disjoint P(AꓴB) = 0.6+0.7 = 1.3

And Since probability cannot be greater than 1, these two mentioned events cannot be disjoint.

 

2) Alice has 2 kids and one of them is a girl. What is the probability that the other child is also a girl? You can assume that there are an equal number of males and females in the world.

A) 0.5 B) 0.25 C) 0.333 D) 0.75 Solution: (C)

The outcomes for two kids can be {BB, BG, GB, GG}

Since it is mentioned that one of them is a girl, we can remove the BB option from the sample space. Therefore the sample space has 3 options while only one fits the second condition. Therefore the probability the second child will be a girl too is 1/3.

 

3) A fair six-sided die is rolled twice. What is the probability of getting 2 on the first roll and not getting 4 on the second roll?

A) 1/36 B) 1/18 C) 5/36 D) 1/6 E) 1/3 Solution: (C)

The two events mentioned are independent. The first roll of the die is independent of the second roll. Therefore the probabilities can be directly multiplied.

P(getting first 2) = 1/6

P(no second 4) = 5/6

Therefore P(getting first 2 and no second 4) = 1/6* 5/6 = 5/36

 

4) 

A) True B) False Solution: (A)

P(AꓵCc) will be only P(A). P(only A)+P(C) will make it P(AꓴC). P(BꓵAcꓵCc) is P(only B) Therefore P(AꓴC) and P(only B) will make P(AꓴBꓴC)

 

5) Consider a tetrahedral die and roll it twice. What is the probability that the number on the first roll is strictly higher than the number on the second roll?Note: A tetrahedral die has only four sides (1, 2, 3 and 4). 

A) 1/2 B) 3/8 C) 7/16 D) 9/16 Solution: (B)

(1,1) (2,1) (3,1) (4,1)

(1,2) (2,2) (3,2) (4,2)

(1,3) (2,3) (3,3) (4,3)

(1,4) (2,4) (3,4) (4,4)

There are 6 out of 16 possibilities where the first roll is strictly higher than the second roll.

 

6) Which of the following options cannot be the probability of any event? 

A) -0.00001 B) 0.5 C) 1.001 A) Only A B) Only B C) Only C D) A and B E) B and C F) A and C Solution: (F)

Probability always lie within 0 to 1. 

 

7) Anita randomly picks 4 cards from a deck of 52-cards and places them back into the deck ( Any set of 4 cards is equally likely ). Then, Babita randomly chooses 8 cards out of the same deck ( Any set of 8 cards is equally likely). Assume that the choice of 4 cards by Anita and the choice of 8 cards by Babita are independent. What is the probability that all 4 cards chosen by Anita are in the set of 8 cards chosen by Babita?

A)48C4 x 52C4 B)48C4 x 52C8 C)48C8 x 52C8

D) None of the above

Solution: (A)

The total number of possible combination would be 52C4 (For selecting 4 cards by Anita) * 52C8 (For selecting 8 cards by Babita).

स्रोत : www.analyticsvidhya.com

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A small company employs 3 men and 5 women. If a team of 4

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A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 women?

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3.2.2 Probability sampling

Statistics: Power from Data! is a web resource that was created in 2001 to assist secondary students and teachers of Mathematics and Information Studies in getting the most from statistics. Over the past 20 years, this product has become one of Statistics Canada most popular references for students, teachers, and many other members of the general population. This product was last updated in 2021.

3.2 Sampling

3.2.2 Probability sampling

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3 Data gathering and processing

3.2 Sampling

3.2.1 Selection of a sample

3.2.2 Probability sampling

3.2.3 Non-probability sampling

Probability sampling refers to the selection of a sample from a population, when this selection is based on the principle of randomization, that is, random selection or chance. Probability sampling is more complex, more time-consuming and usually more costly than non-probability sampling. However, because units from the population are randomly selected and each unit’s selection probability can be calculated, reliable estimates can be produced and statistical inferences can be made about the population.

There are several different ways in which a probability sample can be selected.

When choosing a probability sample design, the goal is to minimize the sampling error of the estimates for the most important survey variables, while simultaneously minimizing the time and cost of conducting the survey. Some operational constraints can also have an impact on that choice, such as characteristics of the survey frame.

In the present section, each of these methods will be described briefly and illustrated with examples.

Simple random sampling

In simple random sampling (SRS), each sampling unit of a population has an equal chance of being included in the sample. Consequently, each possible sample also has an equal chance of being selected. To select a simple random sample, you need to list all of the units in the survey population.

Example 1

To draw a simple random sample from a telephone book, each entry would need to be numbered sequentially. If there were 10,000 entries in the telephone book and if the sample size was 2,000, then 2,000 numbers between 1 and 10,000 would need to be randomly generated by a computer. All numbers would have the same chance of being generated by the computer. The 2,000 telephone entries corresponding to the 2,000 computer-generated random numbers would make up the sample.

SRS can be done with or without replacement. An SRS with replacement means that there is a possibility that the sampled telephone entry may be selected twice or more. Usually, the SRS approach is conducted without replacement because it is more convenient and gives more precise results. In the rest of the text, SRS will be used to refer to SRS without replacement, unless stated otherwise.

SRS is the most commonly used method. The advantage of this technique is that it does not require any information on the survey frame other than the complete list of units of the survey population along with contact information. Also, since SRS is a simple method and the theory behind it is well established, standard formulas exist to determine the sample size, the estimates and so on, and these formulas are easy to use.

On the other hand, this technique necessitates a list of all units of the population. If such a list doesn’t already exist and the target population is large, it can be very expensive or unrealistic to create one. If a list already exists and includes auxiliary information on the units, then the SRS is not taking advantage of information that allows other methods to be more efficient (like stratified sampling, for example). If collection has to be made in-person, SRS could give a sample that is too spread out across multiple regions, which could increase costs and duration of the survey.

Example 2

Imagine that you own a movie theatre and you are offering a special horror movie film festival next month. To decide which horror movies to show, you survey moviegoers to ask them which of the listed movies are their favorites. To create the list of movies needed for your survey, you decide to sample 10 of the 100 best horror movies of all time. One way of selecting a sample would be to write all of the movie titles on slips of paper and place them in an empty box. Then, draw out 10 titles and you will have your sample. By using this approach, you will have ensured that each movie had an equal probability of selection. You could even calculate this probability of selection by dividing the sample size (n=10) by the population size of the 100 best horror movies of all time (N=100). This probability would be 0.10 (10/100) or 1 in 10.

Systematic sampling

Systematic sampling means that there is a gap, or interval, between each selected unit in the sample. For instance, you could follow these steps:

Number the units on your frame from 1 to N (where N is the total population size).

Determine the sampling interval (K) by dividing the number of units in the population by the desired sample size. For example, to select a sample of 100 from a population of 400, you would need a sampling interval of 400/100 = 4. Therefore, K = 4. You will need to select one unit out of every four units to end up with a total of 100 units in your sample.

Select a number between one and K at random. This number is called the random start and it would be the first number included in your sample. If you choose 3, the third unit on your frame would be the first unit included in your sample; if you choose 2, your sample would start with the second unit on your frame.

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