Question 1

A family has 3 children,2 girls and a boy.Every morning (Tuesday through Saturday)each child selects a stock at random from the list printed in the newspaper.If the stock is up,that child does the morning dishes.If the stock is down,the child who picked the stock does the noon dishes.If the stock is unchanged,that child does the evening dishes.If there is a tie-2 children to do the noon dishes,for example-then both children work together to do the noon dishes,and the remaining meal's dishes are done by default by mom or dad.The assignments can be thought of as an ordered triple,ordered by age.For example,(+,0,-)means that the youngest does the morning dishes (the stock was up),the oldest child does the noon dishes (the stock was down),and the middle child,whose stock was unchanged,does the dishes after the evening meal.(-,0,0)means the youngest does the noon dishes,the other two work together on the dishes from the evening meal.The morning dishes are done by mom and dad.Determine the following events:
(a)  
= {the oldest and youngest work together doing the dishes; the middle child does the dishes from a different meal}
(b)  
= {the youngest child has the day off}
(c)  
= {mom and dad do the dishes twice}
(d)  
= {the oldest child does the noon dishes alone}
(e)  
(f)  
∪  
(g)Let  
= {either the oldest or the youngest child does the morning dishes alone}
Let  
= {the middle child does the evening dishes alone}  
∩  
(h)  
∩  
(i)  
∪  
(j)  
∩

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Question 2

If P(E)= 0.3,P(F)= 0.4,  
P(E ∩ 
F).
F)= 0.2, find P(E ∪

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P(E ∩...

Question 3

Three fair coins are tossed.Find the probability that
(a)three tails show;
(b)exactly two tails show.

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Question 4

A family is having a group picture taken to mail to all the relatives.Mother,Father,Son,and Daughter are being photographed,but somebody has to work the camera,so only 3 people at a time can be photographed.Last year's pictures looked "funny" for some reason,so this year they decide to sit next to each other in various orders to see which composition is best.Let the ordered 4-tuple (M,D,S,
B) represent the photographer (Mom here), the person on the left in the picture (Dad here), the person in the middle in the picture (the Sister, in this case), and the person sitting on the right (Brother here). Determine the following events:
(a)  = {Dad, the tallest, sits in the middle}
(b)  = {the photographer is male and Mom is on the left}
(c)  = {there is only one female in the picture}
(d)  = {Dad is to the immediate left of Mom}
(e)  
(f)  ∪  
(g)  ∩  
(h)  ∩  
(i)  ∪  
(j)  ∩

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Question 5

An urn contains two red and three green marbles.Two marbles are randomly drawn in succession without replacement.Determine the probability that
(a)the first marble is red and the second is green;
(b)both marbles are red.

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Question 6

An office worker spends each coffee break at the same deli.This deli has the same 8 varieties of coffee every day.To add variety and excitement to his or her day,the office worker decides to randomly choose a coffee variety in the morning and then randomly choose a variety in the afternoon.How many morning coffee - afternoon coffee choices are there?

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Question 7

An urn contains ten marbles numbered 1 through 10.If a marble is randomly selected from the urn,determine the probability that it shows a number greater than or equal to 4.

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Question 8

A card is randomly drawn from an ordinary deck of 52 playing cards.What is the probability that it is
(a)a king;
(b)not a heart;
(c)a 10 and not red.

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Question 9

Two fair dice are rolled.What is the probability that the sum of the dots appearing is
(a)2;
(b)7?

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Question 10

A man has a $1,a $5,a $10,and a $20 bill in his billfold.He also has a penny,a nickel,a dime,and a quarter in his pants pocket.He decides to treat himself by spending one bill and one coin.How many spending possibilities does he have?

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Question 11

Two cards are randomly drawn with replacement from a standard deck of 52 playing cards.Find the probability that
(a)both cards are aces;
(b)the first card is red and the second card is a club;
(c)one card is red and the other is a club.

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Question 12

A state has decided to issue personalized license plates with 3 letters on them.The original idea was that these letters would represent the vehicle owner's first,middle,and last initials,respectively.Unfortunately,some 3 letter combinations are more colorful than others and the state received requests for combinations that in no way resembled the person's initials.The Department of Motor Vehicles decided to withdraw inappropriate or suggestive combinations.How long was the list of personalized plates that had to be reviewed?

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Question 13

A man has a $1,a $5,a $10,and a $20 bill in his billfold.He also has a penny,a nickel,a dime,and a quarter in his pants pocket.He decides to treat himself by spending one bill and one coin.Determine the following events.
(a)  
= { the amount of money the man is prepared to spend,expressed in cents,is a prime number}
(b)  
= {the amount of money the man is prepared to spend is more than one third of all the money he is carrying}
(c)  
= {the man spends the nickel}
(d)  
= {the amount to be spent is one half the amount to be spent under another selection}
(e)  
(f)  
∪  
(g)  
∩  
(h)  
∩  
(i)  
∪  
(j)  
∩

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Question 14

A fair coin is tossed and then a fair die is rolled.Determine the probability that
(a)a head and an odd number show;
(b)a 2 or 4 shows.

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Question 15

If the probability that a certain horse wins a race is  
,find the odds that this event occurs.

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Question 16

A plane flies from New York to Chicago,from Chicago to Denver,and from Denver to Los Angeles.The plane's on-time,late,or early departure from each city is recorded as 0 or - or +,respectively.For example,(+,-,0)represents the plane leaving earlier than its scheduled departure time from New York,later than its scheduled departure time from Chicago,and on-time from Denver.Assume that the time ahead of schedule or behind schedule is the same so that the pilot can make up for a late departure.For example,(-,0,+)means the plane was x minutes late out of New York,on-time out of Chicago,and made up the x minutes late out of New York by leaving Denver x minutes early.The plane is,therefore,on time when it arrives in Los Angeles.Determine the following events:
(a)  
= {the plane arrives in L.A.on time}
(b)  
= {the plane is late on arrival in L.A.}
(c)  
= {the plane is on time when it arrives at Denver}
(d)  
= {the plane arrives in L.A.as late as possible}
(e)  
(f)  
∪  
(g)  
∩  
(h)  
∩  
(i)  
∪  
(j)  
∩

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Question 17

A state legislative body is considering an action that allows gambling within the state.An opinion survey of 200 voters was conducted and the results are indicated in the following table:
Favor Oppose No Opinion Total
Democrat 40 35 9 84
Republican 60 30 6 96
Other 4 8 8 20
Total 104 73 23 200
Assume that the survey reflects the opinion of the voting population.If a person is selected at random,determine each of the following (empirical)probabilities:
(a)P (opposes gambling)
(b)P (Republican)
(c)P (Democrat who favors gambling).

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Question 18

If a pair of dice are rolled,the probability that the sum of the numbers of dots appearing is 5 is

Accepted Answer

There are a total of 36 possible outcomes when two dice are rolled (6 possible outcomes for the first die and 6 possible outcomes for the second die). To get a sum of 5, the possible outcomes are (1,4), (2,3), (3,2), and (4,1). Therefore, there are 4 possible outcomes out of 36 possible outcomes. So, the probability of getting a sum of 5 is 4/36 which simplifies to 1/9. The answer choice that represents this probability is B.

Question 19

An urn contains ten marbles numbered 1 through 10.If two marbles are randomly drawn in succession without replacement,determine the probability that
(a)the first marble drawn shows 1 and the second shows 2;
(b)both show an odd number;
(c)at least one marble shows a number greater than 5.

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Question 20

A United Nations diplomat can travel from Washington,D.C.to New York City in 6 ways.Depending on the urgency of the trip,she can fly by helicopter,fly by plane,drive the car to a suburban subway station and then take the subway the rest of the way,drive by limousine,take the train,or borrow a friend's yacht and sail most of the way.When she returns to Washington,D.C.,the same modes of transportation are available.How many round trip transportation combinations are available to her?

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Quiz 9: Introduction to Probability and Statistics

If P(E)= 0.3,P(F)= 0.4, P(E ∩ F). F)= 0.2, find P(E ∪

Three fair coins are tossed.Find the probability that (a)three tails show; (b)exactly two tails show.

An urn contains two red and three green marbles.Two marbles are randomly drawn in succession without replacement.Determine the probability that (a)the first marble is red and the second is green; (b)both marbles are red.

An urn contains ten marbles numbered 1 through 10.If a marble is randomly selected from the urn,determine the probability that it shows a number greater than or equal to 4.

A card is randomly drawn from an ordinary deck of 52 playing cards.What is the probability that it is (a)a king; (b)not a heart; (c)a 10 and not red.

Two fair dice are rolled.What is the probability that the sum of the dots appearing is (a)2; (b)7?

A man has a $1,a $5,a $10,and a $20 bill in his billfold.He also has a penny,a nickel,a dime,and a quarter in his pants pocket.He decides to treat himself by spending one bill and one coin.How many spending possibilities does he have?

Two cards are randomly drawn with replacement from a standard deck of 52 playing cards.Find the probability that (a)both cards are aces; (b)the first card is red and the second card is a club; (c)one card is red and the other is a club.

A fair coin is tossed and then a fair die is rolled.Determine the probability that (a)a head and an odd number show; (b)a 2 or 4 shows.

If the probability that a certain horse wins a race is ,find the odds that this event occurs.

If a pair of dice are rolled,the probability that the sum of the numbers of dots appearing is 5 is

An urn contains ten marbles numbered 1 through 10.If two marbles are randomly drawn in succession without replacement,determine the probability that (a)the first marble drawn shows 1 and the second shows 2; (b)both show an odd number; (c)at least one marble shows a number greater than 5.