Probability Help Please

*3. Suppose A, B are events with p(A) = p, p(B) = 2p, p(A U B) = 0.75

a) Evaluate p(A), p(A ∩ B) and p(A│B) if A and B are mutually exclusive events.

b) Evaluate p(A), p(A ∩ B) and p(A│B) if A and B are independent events.

* 4. A restaurant manager classifies customers as well dressed, moderately dressed or poorly dressed and finds that 50%, 40% and 10% respectively fall into these categories. The manager found that wine was ordered by 70% of the well dressed, by 50% of the moderately dressed and by 30% of the poorly dressed.

a) What is the probability that a randomly chosen customer orders wine?

b) If wine is ordered, what is the probability that the person ordering is well dressed?

c) If wine is not ordered, what is the probability that the person ordering is poorly dressed?

(edited 10 years ago)

Reply 1

jonathan10

OP

bump

Reply 2

jonathan10

OP

bump

Reply 3

ghostwalker

17

Original post by jonathan10

bump

Couple of things to start.

Do familiarise yourself with the guidelines here on posting questions.

And there's little point in bumping a thread if it's still showing on the first page of the forum. It only makes you look desparate and also gives the impression that someone has already replied to the thread.

That said:

For 2, focus on the complementary event. What's the probability that the chain doesn't fail.

For 3, in both case, see what you can work out.
You should have a formula for

P(A\cup B)

And consider what events being mutually exclusive, or being independent means, in terms of probability.

For 4, make a probability tree.

Reply 4

jonathan10

OP

Original post by ghostwalker

Couple of things to start.

Do familiarise yourself with the guidelines here on posting questions.

And there's little point in bumping a thread if it's still showing on the first page of the forum. It only makes you look desparate and also gives the impression that someone has already replied to the thread.

That said:

For 2, focus on the complementary event. What's the probability that the chain doesn't fail.

For 3, in both case, see what you can work out.
You should have a formula for

P(A\cup B)

And consider what events being mutually exclusive, or being independent means, in terms of probability.

For 4, make a probability tree.

Hi thanks a lot for the reply

For 3, would I be right in saying that P(A) = 0.25, P(B) = 0.50, and for A) because they are mutually exclusive P(A AND B) = 0 so therefore P(B|A) = 0?

The answer I'm getting does not sound right :/

(edited 10 years ago)

Reply 5

ghostwalker

17

Original post by jonathan10

Hi thanks a lot for the reply

For 3, would I be right in saying that P(A) = 0.25, P(B) = 0.50, and for A) because they are mutually exclusive P(A AND B) = 0 so therefore P(B|A) = 0?

The answer I'm getting does not sound right :/

Those are correct for 3A.

Note: For 3B, you'll need to solve a quadratic to get the value of "p".

(edited 10 years ago)

Reply 6

jonathan10

OP

Original post by ghostwalker

Those are correct for 3A.

Note: For 3B, you'll need to solve a quadratic to get the values of "p".

Oh thanks for 3A :smile:

For B, how do I solve a quadratic to get the values of "p"? We haven't covered this really... is there a formula I can use here? I was planning to use the same values again and multiply the products of p(A) and (B) to get P(A AND B) = 0.125 :eek:

Reply 7

ghostwalker

17

Original post by jonathan10

Oh thanks for 3A :smile:

For B, how do I solve a quadratic to get the values of "p"? We haven't covered this really... is there a formula I can use here? I was planning to use the same values again and multiply the products of p(A) and (B) to get P(A AND B) = 0.125 :eek:

You need to use the formula for P(AuB) = P(A) + ..., together with the fact that A,B are independent in 3B.

Once you have the quadratic in "p", it's no different to solving any other quadratic, except the only valid values of p are between 0 and 1 - this will allow you to eliminate one solution.

(edited 10 years ago)

Reply 8

TenOfThem

18

Original post by jonathan10

Suppose A, B are events with p(A) = p, p(B) = 2p, p(A U B) = 0.75

a) Evaluate p(A), p(A ∩ B) and p(A│B) if A and B are mutually exclusive events.

b) Evaluate p(A), p(A ∩ B) and p(A│B) if A and B are independent events.