Independent, Dependent, and Conditional Probability
Is this example Independent or Dependent?
.225x.118=.02655
Independent
For the following situation, determine whether to use a permutation or combination.
Selecting a president, vice president, and secretary out of 12 qualified candidates.
Permutation
Determine if the following event is mutually exclusive or overlapping
The 1st event: the number is greater than three
The 2nd event: the number is even
Overlapping
Make a tree diagram for this situation
A coin is flipped then a six-sided dice is rolled.
Heads < 1,2,3,4,5,6
<
Tails < 1,2,3,4,5,6
You go to the doctor and find out that you have cancer but later on they figure out that you never actually did.
Is this a false positive or negative?
False Positive
In a standard deck of cards if you were to pick out a black card and a king of spades would this be independent of dependent?
Dependent
How many ways can you select a hand of three cards from a standard 52-card deck?
22,100 ways.
Determine if the following event is mutually exclusive or overlapping
The 1st event: the person is a senior
The 2nd event: the person is a junior
Mutually Exclusive
The events A and B involve numbers 1 through 10,
A={1,2,3,4,5,6}
B={1,3,7,8}
Represent the 2 events in a Venn Diagram
A={2,4,5,6}
Both={1,3}
B={7,8}
Neither={9,10}
Bob has 5 shirts, 4 pants, and 3 ties from which to choose an outfit. How many ways can he select one shirt, one pair of pants, and a tie?
60 ways.
In a bag there is 5 red marbles and 5 blue marbles
What is the Probability of drawing a red marble and a blue marble without replacement?
5/18
How many arrangements of the letters in the word PERRY are possible?
60 arrangements.
In a school, 30 students are taking Pre-Calculus, 25 are taking Algebra II, and 10 are taking both.
What is the probability that a student chosen at random is taking either Pre-Calculus or Algebra II?
9/11 or .82
The Venn diagram shows the distribution of seta A and B
A={2}
Both={1}
B={6}
Neither={3}
Transform the information into a Two Way Table
A Not Total
B 1 6 7
Not 2 3 5
Total 3 9 12
A horse race has 10 horses how many ways can 1st, 2nd, and 3rd place occur?
720
There are 5 red marbles and 7 blue marbles in a bag, what is the probability of drawing 2 red marbles WITHOUT replacement?
Is this event independent or dependent?
5/33
It is dependent.
In a group of 15 people, three 10$ prizes will be handed out. How many can the prizes be distributed.
15 C 3
455
Mutually Exclusive or Overlapping? why?
Drawing a diamond and drawing a 7.
Overlapping because there can be a 7 of diamonds.
From a group of 15 hockey players at a game of hockey, 13 played on the ice, 7 sat on the bench, and 5 both played and sat on the bench. A hockey player is chosen at random from the team.
A= The person played on the ice
B= The person sat on the bench
Represent this information in a 2-way table
A not A Total
B 5 2 7
Not A 8 0 8
Total 13 2 15
In the word TELEVISION, find the probability the letter is...
a) an E
b) not an E
c) an E or V
Simplify answer to the most simplified fraction.
a) 1/5
b) 4/5
c) 3/10
A die is rolled twice and a coin is tossed twice. What is the probability that the die will turn 6 both times and the coin will land tails both times.
1/144
In a chess tournament there are 100 people the top 5 people will win a prize. How many ways can 1st, 2nd, 3rd, 4th, and 5th be distributed?
100 P 5
9034502400
A bag of marbles has
10 white marbles numbered 1-10
10 purple marbles numbered 1-10
10 turquoise marbles numbered 1-10
10 pink marbles numbered 1-10
A= drawing a purple marble first
B= drawing a 7 second
Find the probability of drawing a purple marble first and a 7 second, if you REPLACE the marble in the bag between draws.
1/4 or .25
At an ice cream store 15 people went today. 10 people ordered vanilla 10 people ordered chocolate and 5 people ordered both.
A= Ordered Vanilla
B=Ordered Chocolate
Create a 2-way table that represents this event.
A Not A Total
B 5 5 10
Not B 5 0 5
Total 10 5 15
A six-sided die is rolled twice, what's the probability of rolling a double?
1/6 of 6/36