# Special Notation

Discussion in 'Probability and Statistics' started by nycmathguy, Jul 10, 2022.

1. ### nycmathguy

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Seeking two example to use the special notation.

nycmathguy, Jul 10, 2022
2. ### MathLover1

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correct

1. X = { 1,2,3} and Y = { 2, 3, 4}, then
X ∪ Y=?
X ∩ Y = ?

2.
If Set X = { 4,6,8,10,12 }, Set Y = { 3,6,9,12,15,18} and Set Z = { 1,2,3,4,5,6,7,8,9,10}. Find the union and intersection of :
1. Set X and Y
2. Set Y and Z
3. Set A and C

MathLover1, Jul 10, 2022
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3. ### nycmathguy

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nycmathguy, Jul 10, 2022
4. ### MathLover1

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why don't you do those above first? these are word problems on sets too

more
3. In a group of 60 people, 27 like cold drinks and 42 like hot drinks and each person likes at least one of the two drinks. How many like both coffee and tea?

4. There are 35 students in art class and 57 students in dance class. Find the number of students who are either in art class or in dance class.

5. In a group of 100 persons, 72 people can speak English and 43 can speak French. How many can speak English only? How many can speak French only and how many can speak both English and French?

Last edited: Jul 10, 2022
MathLover1, Jul 10, 2022
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5. ### nycmathguy

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I will do those tomorrow. I did too much math today. Tired. Brain dead.

nycmathguy, Jul 10, 2022
6. ### nycmathguy

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nycmathguy, Jul 11, 2022
7. ### nycmathguy

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nycmathguy, Jul 11, 2022
8. ### MathLover1

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1. correct

2. If Set X = { 4,6,8,10,12 }, Set Y = { 3,6,9,12,15,18} and Set Z = { 1,2,3,4,5,6,7,8,9,10}. Find the union and intersection of :
1.
X U Y={3,4,6,8,9,10,12,15, 18}
X ∩ Y ={6,12}

2. Set Y and Z
X U Z={ 1,2,3,4,5,6,7,8,9,10,12}
X ∩ Z = { 4,6,8,10 }

3. Set A and C -> this was incomplete, disregard
A U C
=

3. In a group of 60 people, 27 like cold drinks and 42 like hot drinks and each person likes at least one of the two drinks. How many like both coffee and tea?

Using set theory,

n(A∪B) = n(A) + n(B) - n(A∩B)

=> 60 = 27+42-n(A∩B)

=> n(A∩B) = 27+42-60

=> n(A∩B) = 9

4. There are 35 students in art class and 57 students in dance class. Find the number of students who are either in art class or in dance class.

Number of Students in Art Class n(A) = 35

Number of Students in Dance class n(D) = 57

Number of Students in Art & Dance class Both n(A∩D) = 12

number of students who are either in dance class or art class = n( A U D)

n( A U D) = n(A) + n(D) - n(A∩D)

=> n( A U D) = 35 + 57 - 12

=> n( A U D) = 92 - 12

=> n( A U D) = 80

there are 80 students who are either in dance class or art

5. In a group of 100 persons, 72 people can speak English and 43 can speak French. How many can speak English only? How many can speak French only and how many can speak both English and French?

Let A be the set of people who speak English and B be the set of people who speak French.

A - B be the set of people who speak English and not French.

B - A be the set of people who speak French and not English.

A ∩ B be the set of people who speak both French and English.

Given

n(A) = 72 n(B) = 43 n(A ∪ B) = 100

Now, n(A ∩ B) = n(A) + n(B) - n(A ∪ B)

= 72 + 43 - 100

= 115 - 100

= 15

Therefore, number of persons who speak both French and English is = 15

n(A) = n(A - B) + n(A ∩ B)

⇒ n(A - B) = n(A) - n(A ∩ B)

= 72 - 15

= 57

and n(B - A) = n(B) - n(A ∩ B)

= 43 - 15

= 28

Therefore, number of people speaking English only is = 57
Number of people speaking French only is = 28

MathLover1, Jul 11, 2022
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9. ### nycmathguy

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I will stay away from probability and venn Diagram math until the time comes to study the course AFTER Calculus 3, if I decide to do so. I may not even make it through Calculus 1. Math has a special way of humbling the proud. Math has taught me that I am not as smart as I sometimes believe myself to be. OVER AND OUT!!!!!

nycmathguy, Jul 11, 2022
10. ### MathLover1

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you already said several ties that you will stay away from probability, .........remember?

MathLover1, Jul 11, 2022

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