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S1 - Probability

I'm a bit stuck on this probability stuff. In my S1 book there's the question:
If A and B are two event and P(A)=0.6, P(B)=0.3 and P(AuB)=0.8, find:
a) P(AnB)
b) P(A'nB)
c) P(AnB')
d) P(A'nB')
e) P(AuB')
f) P(A'uB)

Well all my answers are wrong. Here's what I did and the answers in the back of the book are in red next to it.
a) P(A)xP(B)=0.18 0.1
b) P(A')xP(B)=0.12 0.2
c) P(A)xP(B')=0.42 0.5
d) P(A'nB')=P(A')xP(B')=0.28 0.2
e) P(AuB')=P(A)+P(B')-P(AnB')=0.88 0.8
f) P(A')+P(B)-P(A'nB)=0.58 0.5

Reply 1

The West Wing

P (AuB) = P(A) + P(B) - P(AnB)

Should solve most of your problems.

Reply 2

insparato

a) You're assuming the events are independent
use the equation P(AuB) = P(a) + P(b) - P(a n b )

0.8 = 0.6 + 0.3 - P(A n B)

P(A n B) = 0.1

b) P(A' n B) = P(b) - P(a n b) = 0.2
c) P (A n B') = P(a) - P (a n b) = 0.5
d) P(A' n B') = 1 - (P(A n B') + P(A' n B) + P(a n b)) = 0.2
e) P( A u B') = P(a) + P('b) - P(A n B') = 0.6 + 0.7 - 0.5 = 0.8
f) P (A' u B) = P(a') + P(b) - P(A' n B) = 0.4 + 0.3 - 0.2 = 0.5

This becomes much easier if you draw a venn diagram.

Reply 3

maffsman

cheers

Reply 4

maffsman

how do you do a venn diagram for that?

Reply 5

maffsman

please can someone tell me how to draw a venn diagram for the problem above

Reply 6

Hingie

See if this diagram helps - this is what a venn diagram actually shows you:

Reply 7

maffsman

ahhh thanks that does help. I was getting confused cos I didn't think of P(A) as being the same as P(AnB')! Thanks mate

Reply 8

Hingie

ooooh no P(A) is NOT NOT NOT the same as P(AnB')... P(AnB') is P(A) minus the intersection (the bit where the two circles cross). P(A) is everything inside that circle, whereas P(AnB') is everything inside that space.

Reply 9

maffsman

lol yeah i noticed that afterwards! Can i ask you a quick question:
I'm trying to find P(S'uT'). I have:
P(S)=0.5
P(T)=0.4
P(SnT)=0.15
P(SnT')=0.1
P(S'nT)=0.25
P(S'nT')=0.5

So what I did was P(S'uT')=P(S')+(T')-P(S'nT')=0.5+0.6-0.5=0.6
But the answer is 0.85, so what is it that I'm doing wrong?

Thanks in advance

Reply 10

insparato

P(S' u T') = P(S') + P(T') - P(S' n T') = 0.5 + 0.6 - 0.25 = 0.85

Reply 11

maffsman

I posted it wrong P(S'nT')=0.5

Reply 12

insparato

You've worked out P(S) wrong, its 0.25.

So P(S' u T') = 0.5 + 0.75 - 0.5 = 0.85

Reply 13

samsonlcy

I find it easiest to actually draw the diagram and use the shading method.

P(A n B) - Because A and B have to happen at the same time so double shaded areas.
Step 1. shade in the areas that have P(A).
Step 2. Now shade areas with P(B).
Step 3. Finally, the "n" sign means, find the areas shaded twice.

P(A u B) - Because A or B have to happen at the same time any shaded areas
Step 1. shade in the areas that have P(A).
Step 2. Now shade areas with P(B).
Step 3. the "u" sign means anything shaded is what you need to find.

When you have P(A' n B') or anything else, do the same steps as above. Easy method!

Reply 14

maffsman

Oh yeah, I have actually got that in my working I just missed out the 2 when I plugged it into my diagram. Cheers mate thought I was going mad lol

And samsonlcy cheers for sharing your method too, I hadn't tried that before, it makes it a lot easier to work out what you need to find and how, so thanks!

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