Probability of Coin Toss Outcomes

The video tutorial explains the difference between probability and likelihood using a coin toss example. It covers the binomial probability distribution, illustrating how to calculate probabilities for different outcomes. The tutorial contrasts probability functions with likelihood functions, showing how to calculate likelihood based on observed data. It also discusses the notations used for probability and likelihood and introduces the concept of maximum likelihood estimation to find parameter values that maximize likelihood.

What is the main difference between probability and likelihood?

• Probability is used to estimate parameters, while likelihood is used to predict outcomes.

• Probability is a measure of the chance of an event, while likelihood is a measure of the chance of a parameter value given data.

• Probability and likelihood are the same concepts.

• Likelihood is used to calculate the probability of an event.

In a binomial distribution, what is the probability of getting one head in eight tosses of a fair coin?

• 50%

• 22%

• 11%

• 3%

What does the binomial probability distribution illustrate?

• The probability of a single coin toss

• The probability of getting a certain number of heads in a series of coin tosses

• The average number of heads in multiple trials

• The likelihood of a parameter value given data

What is the probability of getting two heads in eight tosses of a fair coin?

• 3%

• 11%

• 22%

• 50%

What is the probability of getting three heads in eight tosses of a fair coin?

• 11%

• 3%

• 50%

• 22%

What is the probability of getting five heads in eight tosses of a fair coin?

• 3%

• 11%

• 22%

• 50%

What is the probability of getting four heads in eight tosses of a fair coin?

• 11%

• 3%

• 22%

• 50%

What is the probability of getting zero heads in eight tosses of a fair coin?

• 5.47%

• 1.56%

• 2.34%

• 0.39%

What is the probability of getting eight heads in eight tosses of a fair coin?

• 0.39%

• 1.56%

• 2.34%

• 5.47%

What is the probability of getting six heads in eight tosses of a fair coin?

• 3%

• 15%

• 11%

• 22%