Question 1

A grocery store displays 100 green peppers in 10 rows of 10 each.It is quite likely that customer A's choice of the 2 best peppers to buy would differ from customer B's choice,even if the peppers were more or less identical.In how many ways (sample points)could the first customer to see the green pepper array choose 2 peppers to buy?

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The answer of A grocery store displays 100 green peppers...

Question 2

Determine

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The answer of Determine ...

Question 3

How many distinguishable arrangements of all letters in the word MISSISSIPPI are possible?

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The answer of How many distinguishable arrangements of all letters...

Question 4

From an ordinary deck of 52 playing cards,a two-card hand is dealt.In how many ways can the two cards be of the same face value?

Accepted Answer

There are 13 different face values (Ace through King) in a deck of cards. For each face value, there are 4 cards, and we want to select 2 out of these 4. The number of ways to do this for one face value is $ \binom{4}{2} = 6 $. Since there are 13 different face values, the total number of ways is $ 13 \times 6 = 78 $.

Question 5

In a 20-question examination,each question is worth 5 points and is graded right or wrong.Considering the individual questions,in how many ways can a student score 85 points or higher?

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The answer of In a 20-question examination,each question is worth...

Question 6

Fourteen children from a day care center are the first to arrive at a movie theater that seats 600.They decide to pull a trick on their chaperons by hiding under the seats,one child per seat.If we consider the 14 seats selected to be one "hiding place",how many potential hiding places would the chaperons conceivably have to search? (Leave answer in factorial form.)

Accepted Answer

The answer of Fourteen children from a day care center...

Question 7

A family has two children.Determine
(a)the event  
that at least one child is a boy;
(b)the event  
that at least one child is a girl.
(c)Are  
and  
mutually exclusive?

Accepted Answer

The answer of A family has two children.Determine
(a)the event ...

Question 8

From an urn that contains eight marbles numbered 1 through 8,three marbles are randomly selected in succession and the results observed.Determine the number of sample points in the sample space of this experiment if the marbles are selected
(a)with replacement and
(b)without replacement.

Accepted Answer

The answer of From an urn that contains eight marbles...

Question 9

If S =  
is a sample space of an experiment with events  
  
and  
find

(d)Of the events E,F,and G,which pairs are mutually exclusive?

Accepted Answer

The answer of If S =  
is a sample...

Question 10

If S =  
is a sample space of an experiment with events  
  
and  
find

(e)Of the events E,F,and G,which pairs are mutually exclusive?

Accepted Answer

The answer of If S =  
is a sample...

Question 11

If a die is rolled and then a coin is tossed,and the results are observed,determine the sample space of this experiment.

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The answer of If a die is rolled and then...

Question 12

In a math course of 12 students,the instructor decides that he would like 4 students to go to the board simultaneously to present 4 different problems to the class.How many ways can he choose the 4 students?

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The answer of In a math course of 12 students,the...

Question 13

If S =  is a sample space of an experiment with events E = 
And 
Then E ∩ F' =

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The answer of If S =  is a sample...

Question 14

AN URN CONTAINS FOUR MARBLES,NUMBERS 1,2,3,AND 4.IF A MARBLE IS DRAWN AND THEN A COIN IS TOSSED,AND THE RESULTS are observed,determine the sample space of this experiment.

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The answer of AN URN CONTAINS FOUR MARBLES,NUMBERS 1,2,3,AND 4.IF...

Question 15

A student must select two courses in the liberal arts and three courses in the social sciences.There are six liberal arts courses and ten social science courses,all of which are different,from which the student may choose.How many selections are possible?

Accepted Answer

The number of ways to choose 2 liberal arts courses from 6 is C(6,2) = 15. The number of ways to choose 3 social science courses from 10 is C(10,3) = 120. The total number of selections is the product of these two, 15 * 120 = 1800.

Question 16

A coin is tossed three times.Determine
(a)the event  
that exactly two heads occur;
(b)the event  
that at least two heads occur;
(c)the event  
that no head occurs.

Accepted Answer

The answer of A coin is tossed three times.Determine
(a)the event...

Question 17

If S =  is a sample space of an experiment with events E = 
And 
Then E ∪ F' =

Accepted Answer

The answer of If S =  is a sample...

Question 18

A car rental agency buys 140 new tires to outfit its 35-vehicle fleet.The tires can be distinguished by their production serial numbers.Suppose the tire dealer delivers the tires and dumps them in a heap.The rental agency's maintenance person selects 4 tires from the heap to put on the first car.How many ways can she select the 4 tires to put on the car?

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The answer of A car rental agency buys 140 new...

Question 19

Two light bulbs are selected from a box of 20 bulbs.For this experiment,how many sample points are in the sample space?

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The answer of Two light bulbs are selected from a...

Question 20

Determine

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The answer of Determine ...

Quiz 9: Introduction to Probability and Statistics

Determine

How many distinguishable arrangements of all letters in the word MISSISSIPPI are possible?

From an ordinary deck of 52 playing cards,a two-card hand is dealt.In how many ways can the two cards be of the same face value?

In a 20-question examination,each question is worth 5 points and is graded right or wrong.Considering the individual questions,in how many ways can a student score 85 points or higher?

A family has two children.Determine (a)the event that at least one child is a boy; (b)the event that at least one child is a girl. (c)Are and mutually exclusive?

From an urn that contains eight marbles numbered 1 through 8,three marbles are randomly selected in succession and the results observed.Determine the number of sample points in the sample space of this experiment if the marbles are selected (a)with replacement and (b)without replacement.

If S = is a sample space of an experiment with events and find (d)Of the events E,F,and G,which pairs are mutually exclusive?

If S = is a sample space of an experiment with events and find (e)Of the events E,F,and G,which pairs are mutually exclusive?

If a die is rolled and then a coin is tossed,and the results are observed,determine the sample space of this experiment.

In a math course of 12 students,the instructor decides that he would like 4 students to go to the board simultaneously to present 4 different problems to the class.How many ways can he choose the 4 students?

If S = is a sample space of an experiment with events E = And Then E ∩ F' =

AN URN CONTAINS FOUR MARBLES,NUMBERS 1,2,3,AND 4.IF A MARBLE IS DRAWN AND THEN A COIN IS TOSSED,AND THE RESULTS are observed,determine the sample space of this experiment.

A student must select two courses in the liberal arts and three courses in the social sciences.There are six liberal arts courses and ten social science courses,all of which are different,from which the student may choose.How many selections are possible?

A coin is tossed three times.Determine (a)the event that exactly two heads occur; (b)the event that at least two heads occur; (c)the event that no head occurs.

If S = is a sample space of an experiment with events E = And Then E ∪ F' =

Two light bulbs are selected from a box of 20 bulbs.For this experiment,how many sample points are in the sample space?

Determine