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Probability

Sample Space and Counting
Principle
Addition
Rule
Multiplication
Rule
Venn
Diagrams
Conditional
Probability
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Shoppers in a large shopping mall are categorized as: male or female, over 30 or under
30, and cash or credit.
Draw a tree diagram for the sample space.

A car model comes with the following choices: 9 colors, with or without AC, with or without sunroof, manual or automatic, with or without spoiler, 16’’, 17’’, or 18’’ wheels, and cloth or leather. How many different models can be purchased?

A social security number consists of nine digits. If the repetition of digits is allowed, but the first digit can’t be a 0, 1, or 2, how many different social security number exist?

A combination lock has a mixture of letters and numbers. There are 5 dials on the lock. The first dial is a letter A through H, the next two dials are digits (no repetition), the fourth dial is a letter M through Z, and the last dial is a digit 3 through
7, how many possible codes are there?

In a group of 92 students, 40 have brown eyes, 35 have hazel eyes, and 17 have blue eyes. As a fraction, what is the probability of selecting a student who has either brown eyes or hazel eyes?

In a group of 92 students, 40 have brown eyes, 35 have hazel eyes, and 17 have blue eyes. As a fraction, what is the probability of selecting a student who has either brown eyes or hazel eyes?

If two dice are rolled, find the probability that the sum of the dice is either a 4 or a 9.

What is the probability of selecting an even number card or a heart when selecting a single card from a standard deck?

To maintain their physical fitness, Americans are exercising more than ever in a variety of ways.
Bradley and Robbins interviewed many Americans to determine how the were exercising. In How
American Exercise, they present the following: 53% jog, 44% swim, 46% cycle, 18% jog and swim, 15% swim and cycle, 17% jog and cycle, and 7% jog, swim, and cycle. If an American who exercises regularly is randomly selected, what is the probability that the person either jogs, swims or cycles to maintain physical fitness?

A six side die is rolled and a coin is tossed. What is the probability of getting a 3 and a
Tails?

A card is drawn from a deck, replaced, and then another card is drawn. What is the probability of drawing a King and a Diamond?

A bag contains 4 red marbles, 8 yellow marbles, and 6 green marbles. If two marbles are drawn, without replacement, what is the probability of getting 2 green marbles?

A single die is rolled three times. What is the probability of getting an even number, then a
3, and then a number greater than 2?

Three cards are drawn from a standard deck. If none of the cards are replaced, what is the probability of getting three face cards?

A teacher took a survey of when students play sports. 10 said they play on Saturday, 12 said they play on Sunday, and 3 said they play both days. Draw a Venn Diagram to represent the survey.

A survey of 100 families regarding technology in their homes came up with the following data: 85 families had a smart phone, 78 families had a computer, 10 families had a tablet, 67 families had a smart phone and computer, 8 families had a computer and tablet, 6 families had a smart phone and tablet, and 5 families had all three. Draw a Venn Diagram of the survey.

Of the 28 student in a class, 12 have a part time job, 22 have a part time job or do regular volunteer work, 4 of the students have a part time job and do regular volunteer work. Find the probability of selected a student who does volunteer work but doesn’t have a part time job.

Using the Venn diagram below, find the following probability:
P(A’)

Using the Venn diagram below, find the following probability:
P(B’ U S)

Given the following:
Determine:

Given the following:
Determine:

A biology teacher gave her students two tests The probability that a student received
1 a score of 90% or above on both tests is
10
The probability that a student received a score of 90% or above on the first test is
1
5
, and the probability that a student received a
1 score of 90% or above on the second test is
2
.
Prove whether the events are independent or dependent.

What is the probability that an author is unsuccessful, given that they are an established author.

Find the following probabilities: a. P(Black Hair ∩ Hazel Eyes) b. P(Red Hair ∪ Blue Eyes) c. P(Green Eyes │ Brown Hair )