Independence in Probability Theory

This text discusses the concept of independence in probability theory. It defines what it means for two events to be independent, and it extends this definition to sets of more than two events. The text also provides some examples of independent and dependent events.

Questions

• What is independence in probability theory?
• How do you determine whether two events are independent?
• What is mutual independence?
• Can you give some examples of independent and dependent events?

Answers

• Independence in probability theory means that the occurrence of one event does not affect the probability of the occurrence of another event.
• To determine whether two events are independent, you can use the following formula:

  “`
  P(A \ B) = P(A) * P(B)
  “`

  If the equation holds, then the events are independent.

• Mutual independence means that all of the events in a set are independent of each other.
• Some examples of independent events are:
  * Flipping a coin twice and getting heads both times.
  * Drawing a card from a deck of cards and getting a heart.
  * Rolling a die and getting a 6.

  Some examples of dependent events are:
  * Flipping a coin twice and getting heads the first time, then tails the second time.
  * Drawing two cards from a deck of cards and getting both hearts.
  * Rolling a die twice and getting a 6 the first time, then a 5 the second time.