Definitions
Probability
Likelihood of something happening
Probability is a measure between
0 and 1
Two rules of addition
Mutually Exclusive
Not Mutually Exclusive
Two rules of multiplication
Dependent
Independent
Sample Space
Set of possible outcomes of a random experiment or event
Second rule of probability?
The sum of all the probabilities for all possible outcomes is equal to 1.
An automobile dealer decides to select a month for its annual sale. Find the probability that it will be September or October.
1/12 + 1/12 = 2/12 = 1/6
OR
0.17 (nearest hundredth) or (2 decimal places)
You roll a single die numbered from 1 to 6 twice. What is the probability of rolling a 6 the first time and an odd number the second?
1/12
OR
0.083 (nearest thousandth) or (3 decimal places)
Mutually Exclusive Events
two or more events that cannot occur at the same time
Third rule of probability?
The probability that an even does not occur is 1 - P(A)
At a community swimming pool there are 2 managers, 8 lifeguards, 3 concession stand clerks and 2 maintenance people. If a person is selected at random, find the probability that the person is either a lifeguard or a manager.
8/15 + 2/15 = 10/15 = 2/3
OR
0.67 (nearest hundredth) or (2 decimal places)
In a math class, 75% of students pass the quiz (event Q). 60% of students use a print textbook (event T) and 40% use the e-book (event E).
Find the probability that a student uses the e-book AND passes the quiz
0.75 x 0.40 = 0.3
OR
75/100 x 40/100 = 3000/10,000 = 0.3
Dependent Events
The outcome of one event affects the probability of the other event.
In other words, one event must occur before another can occur.
A single card is chosen at random from a standard deck of 52 playing cards. What is the probability of choosing a card that is not a diamond?
39/52
3/4
0.75
75%
In a certain town: 70% of households have Cable TV (event C) 55% of households have Netflix (event N) These figures include the fact that 42% of households subscribe to both.
Find the probability that a person subscribes to Cable TV or Netflix
0.70 + 0.55 - 0.42 = 0.83
OR
70% + 55% - 42% = 83%
The numbers 4 through 14 are placed in a bowel and drawn at random then replaced after being drawn. What is the probability of drawing the number 14 and then a number less than 12?
8/121
OR
0.07 (nearest hundredth) or (2 decimal places)
Equally Likely Outcomes
results of a random experiment that have the same probability of occurring, such as heads and tails on a fair coin
P(A) = 0.75 Find P(A’)
0.25
25%
1/4
A recent study of 200 nurses found that of 125 female nurses, 56 had bachelor’s degrees; and of 75 male nurses, 34 had bachelor’s degrees. If a nurse is selected at random, find the probability that the nurse is a female nurse with a bachelor’s degree
125/200 + 90/200 = 159/200
OR
0.795 (nearest hundredth) or (3 decimal places)
A jar contains 8 green marbles and 4 red marbles. Two marbles are randomly drawn, one at a time without replacement.
Find the probability of drawing a green marble followed by another green marble.
8/12 x 7/11 = 14/33
OR
0.42 (nearest hundredth) or (2 decimal places)