# Probability/Statistics Question

• srfriggen
In summary, I attempted to learn what I could about the homework problem for my brother-in-law's statistics class, but I don't think I understood it very well. I don't know how to calculate the line over the A or what the line over the B means. I think the events are not dependent, and are mutually exclusive. Additionally, I don't know how to calculate P(A l B).

#### srfriggen

My brother in law asked me to look at this homework problem for him for a statistics class. He assumes that since I'm taking calculus that I must be able to learn statistics and probability. So I've tried to learn what I can this morning but don't see it going too far.

1. Homework Statement

Suppose that P(A) = .61, P(B) = .42, and P(A $$\cap$$ B) = .14

Calculate the following:

a) P(A $$\cup$$ B)

b.) P(A l B)

c.) P(B l A)

d.) P($$\bar{A}$$ $$\cup$$ B)

e.) P(A l $$\overline{B}$$)

f.) P($$\bar{A}$$ l B)

g) Are A and B independent events? Why or Why not?

h) Are A and B mutually exclusive events? Why or why not?

## The Attempt at a Solution

a) P (A U B) = P(A) + P(B) = .61 + .42 = 1.03. (I feel this is incorrect).

b) I don't know how to calculate or attempt (AlB)

d) I don't know what the line over the A means.

g) The are independent if P(A U B) = P(A)P(B), but .14 not equal to .61 * .42, so not independent.

h) ?

## Homework Equations

3. The Attempt at a Solution

Hi srfriggen!

Use Venn diagrams to find what to add, and what to subtract.

I guess the bar means "not".

A and B are independent if P(A and B) = P(A)P(B).

so they are not dependent since P(A and B) does not equal P(A)P(B)?

How do I know if they are mutually exclusive?

Is the answer to a) .89? P(A)+P(B) - P(A and B)?

And how do I calculate P(A l B)?

This seems like an easy problem, IF, I was taking probability or statistics haha. but I just don't have the time to learn it today. I have a calc II test wednesday that is taking up all my time.

srfriggen said:
so they are not dependent since P(A and B) does not equal P(A)P(B)?

yes
Is the answer to a) .89? P(A)+P(B) - P(A and B)?

yes
How do I know if they are mutually exclusive?

And how do I calculate P(A l B)?

Your brother-in-law should know the definitions of P(A l B), and of "mutually exclusive".

Ok, I think I figured out a few more. Can you let me know if I am correct?...

P(A l B) = P(A or B)/P(B) = .14/.42 = .333

P(B l A) = P(A or B)/P(A) = .14/.61=.229

- Are A and B independent events? Why or why not?
No, b/c P(A or B) does not equal P(A)P(B)

-Are A and B mutually exclusive events? Why or why not?
No, b/c P(A or B) does not equal Zero.

I'll let him figure out the other 3 but I want to make sure I'm sending him the correct answers or I'll never hear the end of it! lol

srfriggen said:
P(A l B) = P(A or B)/P(B) = .14/.42 = .333

P(B l A) = P(A or B)/P(A) = .14/.61=.229

- Are A and B independent events? Why or why not?
No, b/c P(A or B) does not equal P(A)P(B)

-Are A and B mutually exclusive events? Why or why not?
No, b/c P(A or B) does not equal Zero.

Yes, that's all correct, except that every time you've written "or", it should be "and".

haha, I keep getting those symbols confused!