# Quick help, Basic Probability.

#### Justinharry88

##### New member
Hey all,

Just working on some homework and could really use some help with these questions.

Squire Tuck, an underling of King Arthur, has been demoted because of a counting mishap in the treasury and tasked with determining how many men in the town of Yorkshire can use certain weapons. Tuck reported that he talked to 146 men of the town of Yorkshire and obtained the following results:
[FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main]74[/FONT][/FONT][/FONT][/FONT]​
men can use swords
[FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main]52[/FONT][/FONT][/FONT][/FONT]​
men can use bows
[FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main]64[/FONT][/FONT][/FONT][/FONT]​
men can use axes
[FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main]19[/FONT][/FONT][/FONT][/FONT]​
men can use swords and bows
[FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main]21[/FONT][/FONT][/FONT][/FONT]​
men can use swords and axes
[FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main]12[/FONT][/FONT][/FONT][/FONT]​
men can use bows and axes
[FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main]3[/FONT][/FONT][/FONT][/FONT]​
men can use all three
[FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main]4[/FONT][/FONT][/FONT][/FONT]​
men are pansies and can't use any of the three

How many men did Squire Tuck really talk to?

A College student decided to survey people in Scranton on what their favorite color out of red, blue, and yellow was. The following are the results of his survey.
 Age Red (R) Blue (B) Yellow (Y) Totals 21-25 (L) 40 20 15 75 26-35 (M) 25 40 55 120 Over 35 (O) 10 60 20 90 Totals 75 120 90 285

Using the letters given in the table, find the number of people in each set.
1.
[FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Math]R[FONT=MathJax_Size1]⋃[/FONT][FONT=MathJax_Math]O[/FONT][/FONT][/FONT][/FONT][/FONT]​

2.
[FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Math]Y[FONT=MathJax_Size1]⋂[/FONT][FONT=MathJax_Math]L[/FONT][/FONT][/FONT][/FONT][/FONT]​

3.
[FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Math]B[FONT=MathJax_Size1]⋃[/FONT][FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Math]M[/FONT][/FONT][FONT=MathJax_Main][FONT=MathJax_Main]′[/FONT][/FONT][/FONT][/FONT][/FONT][/FONT][/FONT][/FONT]​

4.
[FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main]([FONT=MathJax_Math]R[/FONT][FONT=MathJax_Size1]⋂[/FONT][FONT=MathJax_Math]M[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Size1]⋃[/FONT][FONT=MathJax_Math]Y[/FONT][/FONT][/FONT][/FONT][/FONT]​

Thanks!

#### Subhotosh Khan

##### Super Moderator
Staff member
Hey all,

Just working on some homework and could really use some help with these questions.

Squire Tuck, an underling of King Arthur, has been demoted because of a counting mishap in the treasury and tasked with determining how many men in the town of Yorkshire can use certain weapons. Tuck reported that he talked to 146 men of the town of Yorkshire and obtained the following results:
[FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main]74[/FONT][/FONT][/FONT][/FONT]​

men can use swords
[FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main]52[/FONT][/FONT][/FONT][/FONT]​

men can use bows
[FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main]64[/FONT][/FONT][/FONT][/FONT]​

men can use axes
[FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main]19[/FONT][/FONT][/FONT][/FONT]​

men can use swords and bows
[FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main]21[/FONT][/FONT][/FONT][/FONT]​

men can use swords and axes
[FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main]12[/FONT][/FONT][/FONT][/FONT]​

men can use bows and axes
[FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main]3[/FONT][/FONT][/FONT][/FONT]​

men can use all three
[FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main]4[/FONT][/FONT][/FONT][/FONT]​

men are pansies and can't use any of the three

How many men did Squire Tuck really talk to?

Hint: use Venn diagram and answer following questions:

How many villagers can use ONLY Sword ? .... 74-19-21-3 = 31

How many villagers can use ONLY Bow?

How many villagers can use ONLY Axes?

Continue....

A College student decided to survey people in Scranton on what their favorite color out of red, blue, and yellow was. The following are the results of his survey.
 Age Red (R) Blue (B) Yellow (Y) Totals 21-25 (L) 40 20 15 75 26-35 (M) 25 40 55 120 Over 35 (O) 10 60 20 90 Totals 75 120 90 285

Using the letters given in the table, find the number of people in each set.

1. [FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Math]R[FONT=MathJax_Size1]⋃[/FONT][FONT=MathJax_Math]O........ What is the definition of this expression?[/FONT][/FONT][/FONT][/FONT][/FONT]

2.
[FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Math]Y[FONT=MathJax_Size1]⋂[/FONT][FONT=MathJax_Math]L........ What is the definition of this expression?
[/FONT][/FONT][/FONT][/FONT][/FONT]
3.
[FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Math]B[FONT=MathJax_Size1]⋃[/FONT][FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Math]M[/FONT][/FONT][FONT=MathJax_Main][FONT=MathJax_Main]′........ What is the definition of this expression?
[/FONT][/FONT][/FONT][/FONT][/FONT][/FONT][/FONT][/FONT]
4.
[FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main]([FONT=MathJax_Math]R[/FONT][FONT=MathJax_Size1]⋂[/FONT][FONT=MathJax_Math]M[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Size1]⋃[/FONT][FONT=MathJax_Math]Y........ What is the definition of this expression?
[/FONT][/FONT][/FONT][/FONT][/FONT]

Thanks!

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