Probability Tree Diagrams

A probability tree diagram is a visual representation used to illustrate the possible outcomes of a series of events, showing the probabilities associated with each outcome.

To calculate the total number of outcomes, multiply the number of outcomes for each event together.

A sample space is the set of all possible outcomes of a random experiment.

There are 12 total outcomes (6 outcomes from the die multiplied by 2 outcomes from the coin).

The sample space when rolling a die is {1, 2, 3, 4, 5, 6}.

There are 60 combinations (6 outcomes from the die multiplied by 5 outcomes from the spinner multiplied by 2 outcomes from the coin).

The possible outcomes are: (White Milk, Chocolate Chip Cookies), (White Milk, Oatmeal Cookies), (Chocolate Milk, Chocolate Chip Cookies), (Chocolate Milk, Oatmeal Cookies).

The formula for combinations is C(n, r) = n! / (r!(n - r)!), where n is the total number of items, r is the number of items to choose, and '!' denotes factorial.

Two events are independent if the occurrence of one event does not affect the probability of the other event occurring.

Dependent events can be represented by adjusting the probabilities on the branches of the tree based on the outcomes of previous events.