How do I do this basic probability question

I am so bad with probability it is unbelievable. Here is the question:

"P(A') = 0.6, P(A' n B') = 0.4, P(A n B') = 0.1

Calculate:

A) P(B)
B) P(A n B)
C) P(A u B)"

I am especially interested in the Part A question. How do I go about solving this?

Thanks for all the help.

Reply 1

Arsey

you need to draw a venn diagram

Reply 2

Neoclassical

Arsey

you need to draw a venn diagram

Did that, but still can't figure out P(B).

Reply 3

levantine

well question A) answer is 0.6 recurring. (assuming thatP(A' n B' = P(A and B). all you do is 0.4/0.6=0.66666666667

Can you plz explain in words what B) and C) are supposed to mean?

Reply 4

x_mee_x

P(B) = P(B n A) + P(B u A) - P(A)

i learnt this myself today :biggrin:

for P(A n B) you can use whats given in the formulea book. is this for the s1 exam on thursday? im doing it too

Reply 5

Neoclassical

levantine

well question A) answer is 0.6 recurring. (assuming thatP(A' n B' = P(A and B). all you do is 0.4/0.6=0.66666666667

Can you plz explain in words what B) and C) are supposed to mean?

B) P(A intersection B)
C) P(A union B)

By the way, how did you get P(B) in the first place? Can you explain the logic behind this please :u:

Reply 6

Neoclassical

x_mee_x

P(B) = P(B n A) + P(B u A) - P(A)

i learnt this myself today :biggrin:

for P(A n B) you can use whats given in the formulea book. is this for the s1 exam on thursday? im doing it too

Yes it is, and I haven't done Probability, Normal Distribution or Discrete Random Variables :s:

Although I reckon I can complete Discrete Random Variables. It's just Probability that I'm stuck with.

The problem with the solution is that I haven't got P(A) or P(B n A) or P(B u A) :frown:

Reply 7

username253571

Tunde Onabajo

It has been a long time since I did S1 but I think these are the answers:

P(B) = 1 - [P(A n B') + P(A' n B')] = 1 - 0.5 = 0.5
P(A n B) = 1 - [P(A)' + P(A n B')] = 1 - 0.7 = 0.3

Reply 8

Neoclassical

anonnumber6

It has been a long time since I did S1 but I think these are the answers:

P(B) = 1 - [P(A n B') + P(A' n B')] = 1 - 0.5 = 0.5
P(A n B) = 1 - [P(A)' + P(A n B')] = 1 - 0.7 = 0.3

You are correct :biggrin:

. Can you explain to me your reasoning, especially for P(B).

Never have I given a rep, but I think this will be my first time of doing such. You are a life saver if you can give me the reasoning for P(B) :biggrin:

Reply 9

username253571

Tunde Onabajo

You are correct :biggrin:

It's hard to describe with words so I made a quick picture :wink:

So the total sample space is 1 but we want to find just P(B) which I haven't labbelled but it is the circle on the right. The black area represents the probability we want to find so you can see if you add the first two circles together the circle not included is B so if you do one minus the sum of the first two venn diagrams you get B.

Reply 10

x_mee_x

Tunde Onabajo

Yes it is, and I haven't done Probability, Normal Distribution or Discrete Random Variables :s:

Although I reckon I can complete Discrete Random Variables. It's just Probability that I'm stuck with.

The problem with the solution is that I haven't got P(A) or P(B n A) or P(B u A) :frown:

simple way to solve this, as mentioned above, is to use a venn diagram. it is very unlikely that you would be given this question without enough of the respective probabilities to work out the rest.

having drawn a venn diagram, i worked out that P(A) is 0.4, P(B) is 0.5, and P(A n B) is 0.3. hope this helps and good luck for the exam on thursday