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