Math Help - Boolean Algebra using venn diagram

1. Boolean Algebra using venn diagram

can someone help with this question please

A = Paul is late for school
B = Alan is late for school

P(A)=0.24
P(AB)=0.16
P(not A or B)=0.68

a) Display the information on a venn diagram

b) on a randomlly selceted day, calculate the probabilty that

i) At least one of Paul or Alan is late for school
ii) Alan is late for school

im not sure how to work on P(B) which is question ii

2. Re: Boolean Algebra using venn diagram

Hi seamy20!

Do you have a venn diagram?
You're supposed to fill in all the regions with their respective probabilities....

That would be P(A or B).
Did you find that one?

3. Re: Boolean Algebra using venn diagram

Hey yeah i think i have it but not sure

I think its
p(A) is 0.24 and p(AB) is 0.16 then p(A) only has to be 0.8, this means when there all added it leaves p(b) with 0.8

4. Re: Boolean Algebra using venn diagram

Originally Posted by seamy20
can someone help with this question please
A = Paul is late for school
B = Alan is late for school
P(A)=0.24
P(AB)=0.16
P(not A or B)=0.68
a) Display the information on a venn diagram
b) on a randomlly selceted day, calculate the probabilty that
i) At least one of Paul or Alan is late for school
ii) Alan is late for school

\begin{align*}1 &= x+0.16+y+z\\ \mathcal{P}(B) &= 0.16+y \\x &= \mathcal{P}(A)-0.16\\ \mathcal{P}(A^c\cup B)&= \mathcal{P}(A^c)+ \mathcal{P}(B)- \mathcal{P}(A^c\cap B) \end{align*}.

5. Re: Boolean Algebra using venn diagram

Originally Posted by seamy20
Hey yeah i think i have it but not sure

I think its
p(A) is 0.24 and p(AB) is 0.16 then p(A) only has to be 0.8, this means when there all added it leaves p(b) with 0.8

Looking good!

Btw, I am assuming that with P(not A or B)=0.68 you actually mean P(not(A or B)), just like you showed in your venn diagram.
Note that this is not what Plato assumed.

Now for P(A) only, without P(AB), I believe you calculated it as P(A) - P(AB)=0.24-016.
Only when I calculate that, I get 0.08 instead of 0.8....

6. Re: Boolean Algebra using venn diagram

oohh

right i missed that one, good job, thanks

7. Re: Boolean Algebra using venn diagram

Sure!

Just for the record, I assume you found:
(i) P(A or B)=0.32
(ii) P(B)=0.24

8. Re: Boolean Algebra using venn diagram

Originally Posted by ILikeSerena
Btw, I am assuming that with P(not A or B)=0.68 you actually mean P(not(A or B)), just like you showed in your venn diagram.
Note that this is not what Plato assumed.

NO! It was not what was posted.
What gives the right to change what was posted?
Read the rules. We should work with what was posted.
If it is a mistake, the it up to the OP to correct the post.

9. Re: Boolean Algebra using venn diagram

Originally Posted by Plato
NO! It was not what was posted.
What gives the right to change what was posted?
Read the rules. We should work with what was posted.
If it is a mistake, the it up to the OP to correct the post.
Erm... but then there is no solution.

Btw, where can I find these rules?

10. Re: Boolean Algebra using venn diagram

yeah ilikeserena i got those once i got the diagram thanks. Sorry guys for the confusin with the post just wasnt sure how to write it on the keyborad :-)