Chapter 12: Discrete Probability

Content locked

The catalog is public. Reading this content requires approved access.

12.1 Probability of an event

Standard playing cards

Discrete vs. continuous probability

PARTICIPATION ACTIVITY

The uniform distribution

PARTICIPATION ACTIVITY

Check

Show answer

Check

Show answer

Start

Example 12.1.2: Redundant data storage.

Animation content:

Animation captions:

Example 12.1.3: An example from a 5-card hand.

PARTICIPATION ACTIVITY

Animation content:

Animation captions:

PARTICIPATION ACTIVITY

Additional exercises

EXERCISE

12.2 Unions and complements of events ©zy Books 04/08/25-22:08-2501/James Ding

Animation content:

Animation captions:

PARTICIPATION ACTIVITY

Check Show answer

The complement of an event

Check Show answer

Additional exercises

EXERCISE

12.3 Conditional probability and independence

Animation content:

Animation captions:

PARTICIPATION ACTIVITY

A five-card hand example of conditional probability

The complement of an event and conditional probability

Proof.

PARTICIPATION ACTIVITY

Check Show answer

Check

Show answer

Check

Show answer

CHALLENGE ACTIVITY

Start

Independent events

Animation content:

Animation captions:

Check Show answer

Calculating the probabilities of two independent events

PARTICIPATION ACTIVITY

Mutual independence

Additional exercises

EXERCISE

12.4 Bayes’ theorem

PARTICIPATION ACTIVITY

Animation content:

Animation captions:

Proof.

PARTICIPATION ACTIVITY

Example 12.4.1: Testing for defects in computer chip manufacturing.

Additional exercises

EXERCISE

12.5 Random variables

PARTICIPATION ACTIVITY

Fact 12.5.1: Random variables and probabilities.

PARTICIPATION ACTIVITY

Check

Show answer

Animation captions:

Additional exercises

EXERCISE

12.6 Expectation of a random variable

Animation content:

Animation captions:

Example 12.6.1: Expected winnings from a lottery.

PARTICIPATION ACTIVITY

Check Show answer

PARTICIPATION ACTIVITY

Animation content:

Animation captions:

Check Show answer

CHALLENGE ACTIVITY

Start

Additional exercises

EXERCISE

12.7 Linearity of expectations

Animation content:

Animation captions:

Proof.

PARTICIPATION ACTIVITY

Example 12.7.2: Load balancing.

PARTICIPATION ACTIVITY

Check Show answer

CHALLENGE ACTIVITY

Additional exercises

EXERCISE

12.8 Bernoulli trials and the binomial distribution

PARTICIPATION ACTIVITY

Animation content:

Animation captions:

PARTICIPATION ACTIVITY

The expected number of successes

PARTICIPATION ACTIVITY

Start

Additional exercises

EXERCISE

Source