Question

According to the Venn diagram below, what is P(A or B or C) ?

22/25

23/25

21/25

24/25

Answer 1

It seems to be 1/2 to me, but that is not one of the choices.

Answer 2

http://postimg.org/image/4cn8uon3j/

Answer 3

forgot to post image.

Answer 4

add them all first

Answer 5

50

Answer 6

yes, and how many are there in A or B or C ?

Answer 7

25

Answer 8

50-8 = 42 right ?

Answer 9

A or B or C includes everything that belongs to any or all of A/B/C

Answer 10

That just doesn't make sense to me.

Answer 11

it seems like it must be what is P(A or B or C) + P(A and B) + P(A and C) + P(B and C) + P(A and B and C)

Answer 12

save that formula

Answer 13

you just need to add up all the numbers in A, B, C

Answer 14

that gives u the favorable count n(A or B or C)

Answer 15

P(A or B or C) = n(A or B or C)/n(total)

Answer 16

So as long as it has one of the letters, it is included in P(A or B or C)

Answer 17

P(A U B U C) = P(A) + P(B) + P(C) - P(A^B) - P(B^C) - P(C^A) + P(A^B^C)

Answer 18

yes, the key thing to keep in mind is "A or B" is not an exclusive OR.

Answer 19

But minoz's equation doesn't work here.

Answer 20

`A or B` includes everything in `either A` or `B` or `Both`

Answer 21

Which means that minoz's equation would give a different answer, right?

Answer 22

im not looking at minoz's equation

Answer 23

The equation he provided is the one I was given, but it gives a different answer.

Answer 24

it may give the same answer,
but you're given a venn diagram - the easy way to do it is to take the ratio of favorable and total

Answer 25

He is subtracting the two letter combinations but the answer requires that you add them.

Answer 26

and only subtract the a 8 because it isn't A B or C

Answer 27

the 8*

Answer 28

you're subtracting whatever u have counted twice, u can look up for the derivation of that formula

Answer 29

"A and B" gets counted in both P(A) and P(B)
so in the formula u need to subtract it...

but i feel we're digressing from the original problem

Answer 30

10 + 8 + 7 - 2 - 4 - 5 + 6 - 8 = 12

Answer 31

that equation leaves me with 6/25 probability

Answer 32

btw, @minoz is a lady not a guy, I also made that mistake because I havent meet smart ladies in maths been so smart like her so assumed its a guy
ganeshie8 is right and minoz's formula is correct

Answer 33

Alright ! lets work it using all the glorious formula to convince u that both methods are equivalent :)

Answer 34

ok

Answer 35

FIrst observation on notation : n(A) is NOT the same thing as P(A)

Answer 36

what is n(A)?

Answer 37

you're using both of them interchangeably -
n(A) = number of favorable outcomes for event A
p(A) = probability of event A

Answer 38

both are different things, okay ?

Answer 39

ok

Answer 40

yes

Answer 41

Is this ur formula :

`P(A U B U C) = P(A) + P(B) + P(C) - P(A and B) - P(B and C) - P(C and A) + P(A and B and C)`

?

Answer 42

Okay, lets calculate all the probabilities one by one :

P(A) = ?
P(B) = ?
P(C) = ?
P(A and B) = ?
P(B and C) = ?
P(C and A) = ?
P(A and B and C) = ?

Answer 43

So would P(A) be 22/50?

Answer 44

P(A) = n(A) / n(total)
= 22/50

Answer 45

Ok, I was counting it as 10/50 before

Answer 46

Yes, calculate the remaining stuff

Answer 47

50???

Answer 48

Yes i have noticed that ! you're thinking "or" as "exclusive or" thats the only misinterpretation in ur logic

Answer 49

I understand that. But I still don't see how it's not exclusively a or b or c

Answer 50

thats the definition

Answer 51

@ganeshie8
how should be find total n
i.e, 50 u got

Answer 52

@BMF96 counted all of them and told me they addup to 50

Answer 53

yaa i got it
thank u

Answer 54

So if they asked what is P(A) ? They want to know the probability of A being in the answer, not just A exclusively. Correct?

Answer 55

You got it !!

Answer 56

Ok, that is why I couldn't get it. Thanks so much for your help!

Answer 57

Im glad u took time and nailed it down fully :) yw !