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 6

1

P(5) = 6

1

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 50-50 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=12

1

= 0% = 50% = 100%= 0.5

cannot occur

50-50 chance

certain to occur

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

P(blue)=10

2

5

1

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

P(blue or yellow)=10

3

Suppose you draw one smiley face without looking. Find the probability of choosing a blue and yellow smiley face.

P(blue and yellow)= 0

1 23

46 5

7

8

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(event1) + P(event2) = 1

P(blue)=

P(not blue)=

3

1

6

2

3

2

6

4

13

3

3

2

3

1

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