Tree Diagrams, FCP & Probability

A tree diagram is a graphical representation used to illustrate all possible outcomes of a probability experiment, showing the branching of choices.

Multiply the number of choices at each stage of the experiment. For example, if there are 3 choices for one event and 4 for another, the total outcomes are 3 x 4 = 12.

Probability = (Number of favorable outcomes) / (Total number of possible outcomes).

Probability of yellow = 45 / (45 + 12 + 25 + 7) = 45 / 89.

Theoretical probability is the likelihood of an event occurring based on the possible outcomes in a perfect scenario, calculated using the formula: P(E) = Number of favorable outcomes / Total outcomes.

The probability is (1/2)^3 = 1/8.

Subtract the probability of landing on that outcome from 1. For example, if P(yellow) = 1/8, then P(not yellow) = 1 - 1/8 = 7/8.

There are 7 days in a week and 12 months in a year, so total outcomes = 7 x 12 = 84.

There are 6 faces on each die, so total outcomes = 6 x 6 = 36.

A favorable outcome is an outcome that satisfies the conditions of the event we are interested in.