Thread: Finding Probability of Events

1. Finding Probability of Events

Oh, hello there.
Well then, If 70% of students have blank paper, 30% have both lined and blank paper, and 10% no paper, how many people have just lined paper?
Thanks.

2. Set Theory

Let Set B=students who have blank paper, $\displaystyle P(B)=0.7$
Set L=students who have lined paper, $\displaystyle P(L)=x$

$\displaystyle P({B}\cap{L})=0.3$
$\displaystyle P(not {B}\cup{L})=0.1$
That is, the set of students without paper.

You should draw a Venn diagram illustrate this

$\displaystyle P({B}\cup{L})=1-0.1=0.9$
$\displaystyle P({B}\cup{L})=P(B)+P(L)-P({B}\cap{L})=0.9$
$\displaystyle 0.7+x-0.3=0.9$
$\displaystyle x=0.5$

$\displaystyle P(L)=0.5$
To determine percentage of people with lined paper
$\displaystyle P(L(alone))=P(L)-P({L}\cap{B})=0.5-0.3=0.2$

3. Why thank you kind sir or madam.

4. Originally Posted by Shermert
Oh, hello there.
Well then, If 70% of students have blank paper, 30% have both lined and blank paper, and 10% no paper, how many people have just lined paper?
Thanks.
you have

B denoted to Blank just
L denoted to lined just
N denoted to no paper

$\displaystyle P(B\cup L) = .9$ since there is just 10% have not paper

$\displaystyle P(B\cap L) = .3$ since there is 30% have blank and lined

$\displaystyle P(B) = .7$ since there is 70% have just the blank

use

$\displaystyle P(A\cup B) = P(A) + P(B) - P(A\cap B )$

I think it is now easy

5. Originally Posted by I-Think
Let Set B=students who have blank paper, $\displaystyle P(B)=0.7$
Set L=students who have lined paper, $\displaystyle P(L)=x$

$\displaystyle P({B}\cap{L})=0.3$
$\displaystyle P(not {B}\cup{L})=0.1$
That is, the set of students without paper.

You should draw a Venn diagram illustrate this

$\displaystyle P({B}\cup{L})=1-0.1=0.9$
$\displaystyle P({B}\cup{L})=P(B)+P(L)-P({B}\cap{L})=0.9$
$\displaystyle 0.7+x-0.3=0.9$
$\displaystyle x=0.5$

$\displaystyle P(L)=0.5$
To determine percentage of people with just lined paper
$\displaystyle P(L(alone))=P(L)-P({L}\cap{B})=0.5-0.3=0.2$
I like to explain more see the red world