Theoretical Probability WORDS: The ratio of the number of ways the event can occur to the number of possible outcomes. SYMBOLS: number of ways the event can occur number of possible outcomes P (event ) =

Outcome – Possible results of a probability event. Event – A specific outcome or type of outcome. Sample Space – The set of all possible outcomes.

There are six equally likely outcomes on a die. The specific number you are trying to roll is the event. The set of all possible outcomes (1,2,3,4,5,6) is the sample space.

The probability of rolling a 5 on a die is P(5) =

The probability that an event will occur is a number from 0 to 1. A probability of 0 means that the event cannot occur. A probability of ½ means that there is a chance that the event will occur. A probability of 1 means that the event is certain to occur. The closer a probability is to 1, the more likely the event is to occur.

The probability of an event can be expressed as a fraction, decimal, or percent. P=0 P=P= P=1 = 0%= 50%= 100% = 0.5 cannot occur chance certain to occur

Suppose you draw one smiley face without looking. Find the probability of choosing a blue smiley face. P(blue)=

Suppose you draw one smiley face without looking. Find the probability of choosing a blue or yellow smiley face. P (blue or yellow) =

Suppose you draw one smiley face without looking. Find the probability of choosing a blue and yellow smiley face. P (blue and yellow) = 0

Find the probability of each event. P (greater than 5) = P (greater than 10) = P (less than 9) = 3/8 0 8/8 = 1

Complementary Events Two events in which either one or the other must take place, but they cannot both happen at the same time. The sum of their probabilities is 1. P(event 1 ) + P(event 2 ) = 1

P(blue)= P(not blue)= Complementary Events

A meteorologist predicts a 30% chance of rain. What is the probability that it will not rain? P(rain)=30% P(not rain)=70% 30% + 70% = 100% Complementary Events