Question

HELP PLEASE!! Calculate probability of the independent event
P(A or B) when P(a)=.3 and P(B)=.7

Answer 1

You just have to multiply .3 by .7

Answer 2

oh ok well what about conditional probability with the same variables?

Answer 3

$$
P(A\cup B)=P(A)+P(B)-P(A\cap B)
$$
Since A and B are independent, \(P(A\cap B)=0\)
So just SUM the independent probabilities.

Answer 4

so just 1?

Answer 5

Yes.

See - http://en.wikipedia.org/wiki/Inclusion%E2%80%93exclusion_principle

Answer 6

Specifically, this section - http://en.wikipedia.org/wiki/Inclusion%E2%80%93exclusion_principle#In_probability

Answer 7

ok what about if the variables are P(a)=.5 P(b)=.4 and then P(a and b)=.1?????

Answer 8

I'm supposed to calculate the probability

Answer 9

You've got everything you need, P(a), P(b) and P(a and b) -- see my formula above! Just plug in for P(a or b).

Answer 10

$$
P(A\cup B)=P(A)+P(B)-P(A\cap B)=0.5+0.4-0.1
$$
See how I did that?

Answer 11

yes i just thought a and b were supposed to = P(A and B) but the answer is .8

Answer 12

Are you asking me?

Answer 13

yes(:

Answer 14

What are you asking, not sure

Answer 15

the answer is .8 right?

Answer 16

Yes for P(a or b).

Answer 17

ok but theres nothing else i need to find? it just says calculate the probability

Answer 18

Tell me the whole question to be sure

Answer 19

its 27

Answer 20

Oh, those are different problems that P(A or B)

Ok

Answer 21

Do you know what P(A|B) means?

Answer 22

i know its a conditional probability problem

Answer 23

$$
P(A|B)=\cfrac{PA\cap B}{P(B)}=\cfrac{0.1}{0.4}
$$
You can do the next.

BRB

Answer 24

i got .25

Answer 25

Do #27 now

Answer 26

umm isn't that what i did?

Answer 27

oh okay for 27 i got 4

Answer 28

if you can check the other ones i got .21 on 23 and on 25 i got 1 but if you can't then thank you for helping!

Answer 29

Probabilities can not be greater than 1 so #27 is not 4

Answer 30

For #27 what do you have for P(B|A)=P(B and A)/P(A) ?

Answer 31

We already did #23

Answer 32

oh well you had .1/.4 so in 27 i just did .4/.1

Answer 33

No. The "|" does NOT mean division. It means "given" P(A|B) means Probability of event A given event B.

Answer 34

you did .1/.4

Answer 35

$$
P(B|A)=\cfrac{P(A\cap B)}{P(A)}\\
P(A|B)=\cfrac{P(A\cap B)}{P(B)}
$$
Do you see the difference above between the two?

Answer 36

Yes and that one is correct

Answer 37

i guess I'm not understanding this then

Answer 38

So we are dealing with probabilities of events. When we are given that an event occurs, we are asked what is the probability that the other will occur. If they are independent, then there is no effect. But if they are not independent, then conditional probability tells us that
Probability of A given B is the Probability of A and B divided by the probability of B.

Here is a visual

Answer 39

ok

Answer 40

That fraction is
$$
P(A|B)=\cfrac{P(A\cap B)}{P(B)}
$$

Answer 41

that looks like alien writing to me

Answer 42

$$
P(A|B)=P(A \text{ given }B)=\cfrac{P(A\cap B)}{P(B)}=\cfrac{P(A\text{ and }B)}{P(B)}
$$
Is this better?

Answer 43

haha no I'm sorry... what does it look like with the values plugged in