Question

P(A) = .52 P(B) = .45 P(A n B) = .35 Using a venn diagram find the probability of each of the given points
P(A but not B)=
P(B but not A) =
P( A or B) =
P( neither A nor B) =
answers should be exact

Answer 1

Since P(A) = .52 and P(A n B) = .35, the difference of these two will tell you P(A but not B).
Similar for P(B n A).

To get (A or B), you add the answers from the first two. Neither A nor B, you subtract the first two from 1.

Answer 2

so P(A but not B) = .17
P( A or B) = .34
neither a or b = .49

Answer 3

What did you get for (B but not A)?

Answer 4

isn't it also .17?

Answer 5

P(A but not B) = .52 - .35
P(B but not A) = .45 - .35

Answer 6

And I made a mistake for neither A nor B; should be P(A) + P(B) +P(A n B)

Answer 7

Drawing a picture will really help; put .35 in the overlapping area first.

Answer 8

oh oh oh okay! so P(B but not A) = .1
and neither a nor be = 1.32

Answer 9

Probabilities will always take on a value between 0 and 1. For neither A nor B, which could be written as \[P(A ^{c} n B ^{c})\]
(where c stands for complement), you want 1 - P(A) - P(B) + P(A n B)

Answer 10

Except that should be bracketed as 1 - [P(A) - P(B) + P(A n B)]

Thus, I get the probability of neither A nor B to be .38.

Answer 11

If you were to draw this as a Venn Diagram, you would have the overlapping portion of the circles containing .35, which was given as P(A n B).
In circle A, you would have .52-.35 = .17
In circle B, you would have .45-.35 = .10
And outside both circles, you would have 1-[.52 + .45 - .35] = .38

Answer 12

okay so i got new values. P(A) = .50 P(B) = .62 and P(A n B) = .42
P( A but not B)= .92
P(B but not A) = 1.04
P( neither A or B) = ?
P( A and B)= ?

Answer 13

Is this a new problem?

It is not possible for P(A but not B) to be greater than P(A).

For B but not A, remember that probabilities must be between 0 and 1, so that is obviously incorrect.

Answer 14

Start a Venn Diagram with .42 in the overlapping portion of two circles.

Answer 15

i meant P(A but not B)= .08
and for P(B but not A)= .20

Answer 16

Yes! That looks better.
You already have the answer to P(A n B), if that is what you meant to write, as given in the problem: P(A n B) = .42
So, neither A nor B = 1- [P(A) + P(B) - P(A n B)]

Answer 17

and so neither a nor b = .7

Answer 18

That is actually P(A or B). You need to subtract that amount from 1.

P(neither A nor B) = 1- [P(A) + P(B) - P(A n B)]
= 1-[.50 + .62 - .42]

Answer 19

ohhhh so its .3

Answer 20

Yep!

Answer 21

the .42 is incorrect

Answer 22

which is the a or b

Answer 23

P(A n B), I assumed, meant A intersect B, which means A *and* B.

Answer 24

i thought so too. but i guess not

Answer 25

P (A or B) would be P(A but not B) + P(B but not A) + P(A n B) = .7, I think.