Practical Data Science using Python - Binomial Theory - Expected Value and Standard Error

The video tutorial covers the concept of mutually exclusive events and the addition rule for calculating probabilities. It explains how to determine the probability of specific outcomes in dice rolls and introduces the binomial formula for solving probability problems. The tutorial also discusses expected value and standard error, providing examples to illustrate these concepts.

What is the probability of getting either a 2 or a 5 when rolling a fair six-sided die?

• 33.3%

• 66.7%

• 16.7%

• 50%

Which of the following is a requirement for using the addition rule in probability?

• Events must be independent

• Events must occur simultaneously

• Events must be dependent

• Events must be mutually exclusive

In a binomial experiment, what does the binomial coefficient represent?

• The expected value of the experiment

• The total number of trials

• The number of possible outcome patterns

• The probability of a single event

How is the probability of a specific outcome calculated in a binomial experiment?

• By adding the probabilities of all outcomes

• By multiplying the binomial coefficient by the probability of the desired outcome

• By dividing the number of successful outcomes by the total number of trials

• By subtracting the probability of the opposite outcome

What is the expected value of buying 10 tickets in a lottery with 1000 tickets and a single $1000 prize?

• $1000

• $100

• $10

• $1

How is the expected value calculated in a series of experiments?

• By dividing the total number of successful outcomes by the number of trials

• By multiplying the number of events by the average possible value

• By adding the probabilities of all possible outcomes

• By averaging the outcomes of all experiments

What does the standard error measure in a probability experiment?

• The average value of all outcomes

• The deviation of observed values from expected values

• The total number of trials

• The probability of a single event

In the context of standard error, what does the square root law help calculate?

• The expected value of an experiment

• The probability of a specific outcome

• The standard error for a process

• The standard deviation of the values

If the observed value is 71 and the expected value is 75, what is the standard error?

• 0

• 71

• 4

• 75

Which formula is used to calculate the standard error in large samples?

• Standard error equals the difference between observed and expected values

• Standard error equals the sum of observed and expected values

• Standard error equals the square root of the number of draws multiplied by the standard deviation

• Standard error equals the number of draws divided by the standard deviation