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This chapter covers principles of probability. After completing this chapter students should be able to: write sample spaces; determine whether two events are mutually exclusive; use the addition rule; calculate probabilities using tree diagrams and combinations; solve problems involving conditional probability; determine whether two events are independent.

Sample spaces and probability

In problems 1 - 6, write a sample space for the given experiment.

A die is rolled.

1,2,3,4,5,6 size 12{ left lbrace 1,2,3,4,5,6 right rbrace } {}
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A penny and a nickel are tossed.

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A die is rolled, and a coin is tossed.

1H , 2H , 3H , 4H , 5H , 6H , 1T , 2T , 3T , 4T , 5T , 6T size 12{ left lbrace 1H,2H,3H,4H,5H,6H,1T,2T,3T,4T,5T,6T right rbrace } {}
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Two dice are rolled.

1 2 3 4 5 6
1 (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)
2 (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)
3 (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)
4 (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)
5 (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)
6 (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)
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A jar contains four marbles numbered 1, 2, 3, and 4. Two marbles are drawn.

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In problems 7 - 12, a card is selected from a deck. Find the following probabilities.

P an ace size 12{P left ("an ace" right )} {}
4 / 52 size 12{4/"52"} {}
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P a red card size 12{P left ("a red card" right )} {}
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P a club size 12{P left ("a club" right )} {}
13 / 52 size 12{"13"/"52"} {}
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P a face card size 12{P left ("a face card" right )} {}
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P a jack or spade size 12{P left ("a jack or spade" right )} {}
16 / 52 size 12{"16"/"52"} {}
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P a jack and a spade size 12{P left ("a jack and a spade" right )} {}
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A jar contains 6 red, 7 white, and 7 blue marbles. If a marble is chosen at random, find the following probabilities.

P red size 12{P left ("red" right )} {}
6 / 20 size 12{6/"20"} {}
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P white size 12{P left ("white" right )} {}
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P red or blue size 12{P left ("red or blue" right )} {}
13 / 20 size 12{"13"/"20"} {}
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P red and blue size 12{P left ("red and blue" right )} {}
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Consider a family of three children. Find the following probabilities.

P two boys and a girl size 12{P left ("two boys and a girl" right )} {}
3 / 8 size 12{3/8} {}
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P at least one boy size 12{P left ("at least one boy" right )} {}
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P children of both sexes size 12{P left ("children of both sexes" right )} {}
6 / 8 size 12{6/8} {}
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P at most one girl size 12{P left ("at most one girl" right )} {}
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Two dice are rolled. Find the following probabilities.

P the sum of the dice is 5 size 12{P left ("the sum of the dice is 5" right )} {}
4 / 36 size 12{4/"36"} {}
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P the sum of the dice is 8 size 12{P left ("the sum of the dice is 8" right )} {}
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P the sum is 3 or 6 size 12{P left ("the sum is 3 or 6" right )} {}
7 / 36 size 12{7/"36"} {}
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P the sum is more than 10 size 12{P left ("the sum is more than 10" right )} {}
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A jar contains four marbles numbered 1, 2, 3, and 4. If two marbles are drawn, find the following probabilities.

P the sum of the number is 5 size 12{P left ("the sum of the number is 5" right )} {}
4 / 12 size 12{4/"12"} {}
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P the sum of the numbers is odd size 12{P left ("the sum of the numbers is odd" right )} {}
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P the sum of the numbers is 9 size 12{P left ("the sum of the numbers is 9" right )} {}

0

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P one of the numbers is 3 size 12{P left ("one of the numbers is 3" right )} {}
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Mutually exclusive events and the addition rule

Determine whether the following pair of events are mutually exclusive.

A = A person earns more than $25,000 size 12{A= left lbrace "A person earns more than $25,000" right rbrace } {}
B = A person earns less than $20,000 size 12{B= left lbrace "A person earns less than $20,000" right rbrace } {}

Yes

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A card is drawn from a deck.

C = It is a King size 12{C= left lbrace "It is a King" right rbrace } {} D = It is a heart size 12{D= left lbrace "It is a heart" right rbrace } {} .
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A die is rolled.

E = An even number shows size 12{E= left lbrace "An even number shows" right rbrace } {}
F = A number greater than 3 shows size 12{F= left lbrace "A number greater than 3 shows" right rbrace } {}

No

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Two dice are rolled.

G = The sum of dice is 8 size 12{G= left lbrace "The sum of dice is 8" right rbrace } {}
H = One die shows a 6 size 12{H= left lbrace "One die shows a 6" right rbrace } {}
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Three coins are tossed.

I = Two heads come up size 12{I= left lbrace "Two heads come up" right rbrace } {}
J = At least one tail comes up size 12{J= left lbrace "At least one tail comes up" right rbrace } {}

No

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A family has three children.

K = First born is a boy size 12{K= left lbrace "First born is a boy" right rbrace } {}
L = The family has children of both sexes size 12{L= left lbrace "The family has children of both sexes" right rbrace } {}
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Use the addition rule to find the following probabilities.

A card is drawn from a deck, and the events C size 12{C} {} and D size 12{D} {} are as follows:

C = It is a king size 12{C= left lbrace "It is a king" right rbrace } {}
D = It is a heart size 12{D= left lbrace "It is a heart" right rbrace } {}

Find P C   or   D size 12{P left (C" or "D right )} {} .

16 / 52 size 12{"16"/"52"} {}
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A die is rolled, and the events E size 12{E} {} and F size 12{F} {} are as follows:

E = An even number shows size 12{E= left lbrace "An even number shows" right rbrace } {}
F = A number greater than 3 shows size 12{F= left lbrace "A number greater than 3 shows" right rbrace } {}

Find P E   or   F size 12{P left (E" or "F right )} {} .

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Two dice are rolled, and the events G size 12{G} {} and H size 12{H} {} are as follows:

G = The sum of dice is 8 size 12{G= left lbrace "The sum of dice is 8" right rbrace } {}
H = Exactly one die shows a 6 size 12{H= left lbrace "Exactly one die shows a 6" right rbrace } {}

Find P G   or   H size 12{P left (G" or "H right )} {} .

13 / 36 size 12{"13"/"36"} {}
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Three coins are tossed, and the events I size 12{I} {} and J size 12{J} {} are as follows:

I = Two heads come up size 12{I= left lbrace "Two heads come up" right rbrace } {}
J = At least one tail comes up size 12{J= left lbrace "At least one tail comes up" right rbrace } {}

Find P I   or  J size 12{P left (I" or "J right )} {} .

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At De Anza college, 20% of the students take Finite Mathematics, 30% take Statistics and 10% take both. What percentage of the students take Finite Mathematics or Statistics?

40%

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Questions & Answers

differentiate between demand and supply giving examples
Lambiv Reply
differentiated between demand and supply using examples
Lambiv
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appreciation
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In economics, a perfect market refers to a theoretical construct where all participants have perfect information, goods are homogenous, there are no barriers to entry or exit, and prices are determined solely by supply and demand. It's an idealized model used for analysis,
Ezea
What is ceteris paribus?
Shukri Reply
other things being equal
AI-Robot
When MP₁ becomes negative, TP start to decline. Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 • Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of lab
Kelo
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 • Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of labour (APL) and marginal product of labour (MPL)
Kelo
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Shukri
Can I ask you other question?
Shukri
what is monopoly mean?
Habtamu Reply
What is different between quantity demand and demand?
Shukri Reply
Quantity demanded refers to the specific amount of a good or service that consumers are willing and able to purchase at a give price and within a specific time period. Demand, on the other hand, is a broader concept that encompasses the entire relationship between price and quantity demanded
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Fiker Reply
Economic growth as an increase in the production and consumption of goods and services within an economy.but Economic development as a broader concept that encompasses not only economic growth but also social & human well being.
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Jabir
What do you think is more important to focus on when considering inequality ?
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any question about economics?
Awais Reply
sir...I just want to ask one question... Define the term contract curve? if you are free please help me to find this answer 🙏
Asui
it is a curve that we get after connecting the pareto optimal combinations of two consumers after their mutually beneficial trade offs
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In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities, where neither p
Cornelius
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities,
Cornelius
Suppose a consumer consuming two commodities X and Y has The following utility function u=X0.4 Y0.6. If the price of the X and Y are 2 and 3 respectively and income Constraint is birr 50. A,Calculate quantities of x and y which maximize utility. B,Calculate value of Lagrange multiplier. C,Calculate quantities of X and Y consumed with a given price. D,alculate optimum level of output .
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Answer
Feyisa
c
Jabir
the market for lemon has 10 potential consumers, each having an individual demand curve p=101-10Qi, where p is price in dollar's per cup and Qi is the number of cups demanded per week by the i th consumer.Find the market demand curve using algebra. Draw an individual demand curve and the market dema
Gsbwnw Reply
suppose the production function is given by ( L, K)=L¼K¾.assuming capital is fixed find APL and MPL. consider the following short run production function:Q=6L²-0.4L³ a) find the value of L that maximizes output b)find the value of L that maximizes marginal product
Abdureman
types of unemployment
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What is the difference between perfect competition and monopolistic competition?
Mohammed
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Source:  OpenStax, Applied finite mathematics. OpenStax CNX. Jul 16, 2011 Download for free at http://cnx.org/content/col10613/1.5
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