Assignments 5 6

course Mth 151

sorry so late!

????E?????assignment #005

005. Binary probabilities

Liberal Arts Mathematics II

03-20-2008

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21:28:49

`questionNumber 50000

`q001. Note that there are 10 questions in this assignment.

List the possible outcomes if a fair coin is flipped 2 times.

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RESPONSE -->

heads, heads

heads, tails

tails,heads

tails,tails

4possible outcomes

confidence assessment: 3

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21:31:01

`questionNumber 50000

`q002. List the possible outcomes if a fair coin is flipped 3 times.

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RESPONSE -->

8 outcomes

H,H,H

H,H,T

H,T,H

H,T,T

T,H,H

T,H,T

T,T,H

H,H,H

confidence assessment: 3

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21:45:53

`questionNumber 50000

`q003. List the possible outcomes if a fair coin is flipped 4 times.

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RESPONSE -->

16 OUTCOMES

HHHH

HHHT

HHTH

HTHH

HTHT

HTTH

HTTT

THHH

THHT

THTH

THTT

TTHH

TTHT

TTTH

TTTT

confidence assessment: 3

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21:50:18

`questionNumber 50000

`q004. If a fair coin is flipped 4 times, how many of the outcomes contain exactly two 'heads'?

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RESPONSE -->

1&2 HHTT

1&3 HTHT

1&4 HTTH

2&3 THHT

2&4 THTH

3&4 TTHH

4*3/2

C(4,2)=6 POSSIBILITES

confidence assessment: 3

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21:52:48

`questionNumber 50000

`q005. If a fair coin is flipped 7 times, how many of the outcomes contain exactly three 'heads'?

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RESPONSE -->

C(7,3)= 7*6*5/3!

35 WAYS

confidence assessment: 3

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22:02:53

`questionNumber 50000

`q006. If we flip a fair coin 6 times, in how many ways can we get no 'heads'?

In how many ways can we get exactly one 'head'?

In how many ways can we get exactly two 'heads'?

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RESPONSE -->

4 TIMES WITH NO HEADS

1 TIME

2 TIMES

confidence assessment: 0

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22:03:23

`questionNumber 50000

In how many ways can we get exactly three 'heads'?

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RESPONSE -->

4 TIMES

confidence assessment: 3

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22:05:21

`questionNumber 50000

The number of ways to get no 'heads' is C(6,0) = 1.

The number of ways to get exactly one 'head' is C(6,1) = 6.

The number of ways to get exactly two 'heads' is C(6,2) = 15.

The number of ways to get exactly three 'heads' is C(6,3) = 20.

The number of ways to get exactly four 'heads' is C(6,4) = 15.

The number of ways to get exactly five 'heads' is C(6,5) = 6.

The number of ways to get exactly six 'heads' is C(6,6) = 1.

These numbers form the n = 6 row of Pascal's Triangle:

1 6 15 20 15 6 1

See your text for a description of Pascal's Triangle. Note also that these numbers add up to 64, which is 2^6, the number of possible outcomes when a coin is flipped 6 times.

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RESPONSE -->

15 TIMES

6 TIMES

1 TIME

self critique assessment: 2

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22:09:28

`questionNumber 50000

`q007. List all the subsets of the set {a, b}.

Then do the same for the set {a,b,c}.

Then do the same for the set {a,b,c,d}.

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RESPONSE -->

4

6

8

confidence assessment: 2

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22:13:29

`questionNumber 50000

`q008. How many subsets would there be of the set {a, b, c, d, e, f, g, h}?

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RESPONSE -->

256

confidence assessment: 2

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22:17:36

`questionNumber 50000

`q009. How many 4-element subsets would there be of the set {a, b, c, d, e, f, g, h}?

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RESPONSE -->

4 SUB SETS ANS 8 SETS

C(8,4)=8*7*6*5/4*3*2*1=70

confidence assessment: 1

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22:20:26

`questionNumber 50000

`q010. How many subsets of the set {a,b,c,d} contain 4 elements?

How many subsets of the set {a,b,c,d} contain 3 elements?

How many subsets of the set {a,b,c,d} contain 2 elements?

How many subsets of the set {a,b,c,d} contain 1 elements?

How many subsets of the set {a,b,c,d} contain no elements?

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RESPONSE -->

4 ELEMENTS C(4,4)=1

3 ELEMENTS C(4,3)=4

2 ELEMENTS C(4,2)=6

1 ELEMENT C(4,1)=4

0 ELEMENTS C(4,0)=1

confidence assessment: 2

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?+???????W??assignment #006

006. Cards

Liberal Arts Mathematics II

03-20-2008

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22:42:26

`questionNumber 60000

`q001. Note that there are 8 questions in this assignment.

Using a standard deck of cards, in how many ways is it possible to get a hand containing exactly two 5's?

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RESPONSE -->

c(4,2)* c(48,3) ways

confidence assessment: 2

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22:42:59

`questionNumber 60000

`q002. Using a standard deck of cards, in how many ways is it possible to get a hand containing exactly two 5's and exactly two 9's?

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RESPONSE -->

confidence assessment:

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22:43:50

`questionNumber 60000

There are C( 4, 2) ways to select exactly two 5's and C(4, 2) ways to select exactly two 9's. There are 44 remaining cards which are neither 9 nor 5.

The total number of possible ways is therefore C(4, 2) * C(4, 2) * 44.

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RESPONSE -->

c(4,2)* c(4,2)*44

self critique assessment: 2

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22:44:24

`questionNumber 60000

`q003. Using a standard deck of cards, in how many ways is it possible to get a 'full house' consisting of two 5's and three 9's?

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RESPONSE -->

c(4,2)*(4,3)

confidence assessment: 2

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22:45:15

`questionNumber 60000

`q004. Using a standard deck of cards, in how many ways is it possible to get a 'full house' consisting of two 5's and three identical face cards?

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RESPONSE -->

3*c(4,2)*c(4,3)

confidence assessment: 3

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22:46:43

`questionNumber 60000

`q005. Using a standard deck of cards, in how many ways is it possible to get a 'full house' consisting of two of one denomination and three of another?

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RESPONSE -->

13*12*c(4,2)*c(4,3)

confidence assessment: 1

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22:48:15

`questionNumber 60000

`q006. Using a standard deck of cards, in how many ways is it possible to get a 'flush' consisting of five cards all of the same suit?

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RESPONSE -->

4*c(13,5)

confidence assessment: 2

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22:49:18

`questionNumber 60000

`q007. Using a standard deck of cards, in how many ways is it possible to get a 'straight' consisting of exactly one each of the denominations 5, 6, 7, 8 and 9?

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RESPONSE -->

4^5

5 t0 9 possible straights

confidence assessment: 2

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22:50:29

`questionNumber 60000

`q008. Using a standard deck of cards, in how many ways is it possible to get a 'straight' consisting of five cards of consecutive denominations, assuming that the 'ace' can be either 'high' or 'low'?

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RESPONSE -->

10*4^5poss straights

confidence assessment: 2

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Again, be sure to check your work against the solutions given by the Query and qa programs. If there are discrepancies then you should self-critique as previously indicated.