You are Here: Home >< Maths

# Two S1 questions D: Watch

1. Can someone help me with these please?

The three events A, B and C are defined in the same sample space. The events A and C are
mutually exclusive. The events A and B are independent.

Given that P(A) = 2/5, P(C) = 1/3 and P(A U B ) = 5/8 find

(a) P(A U C),

(b) P(B).

(Do i draw 3 circles?)
The events A and B are independent with P(A) = 1/2 and P(A U B) = 2/3
Find
(a) P(B),

(b) P(A|B),

(c) P(B'|A).

(I don't get this mutually exclusive and Independent stuff )
2. (Original post by Jonario)
Can someone help me with these please?

The three events A, B and C are defined in the same sample space. The events A and C are
mutually exclusive. The events A and B are independent.

Given that P(A) = 2/5, P(C) = 1/3 or P(A U B ) = 5/8 find

(a) P(A U C),

(b) P(B).

(Do i draw 3 circles?)
The events A and B are independent with P(A) = 1/2 and P(A U B) = 2/3
Find
(a) P(B),

(b) P(A|B),

(c) P(B'|A).

(I don't get this mutually exclusive and Independent stuff )
I am not sure how to help without just giving the answers, but anyway

P(AUC)= probability of BOTH A and C occuring which is 1/3+2/5

We know

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

but as A and B are independent then P(AnB)=P(A)P(B)

so solving for P(B) we get

5/8= 2/5 + P(B) -p(B)2/5
so P(B)=3/8

For the second question we have:

(a), to find P(B) follow the same process as I have in the previous question, noting A and B are independent.

(b) For conditional probability just use the formula

(c) Do you mean B' is the complement or?
3. (Original post by zcomputer5)
I am not sure how to help without just giving the answers, but anyway

P(AUC)= probability of BOTH A and C occuring which is 1/3+2/5

We know

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

but as A and B are independent then P(AnB)=P(A)P(B)

so solving for P(B) we get

5/8= 2/5 + P(B) -p(B)2/5
so P(B)=9/56

For the second question we have:

(a), to find P(B) follow the same process as I have in the previous question, noting A and B are independent.

(b) For conditional probability just use the formula

(c) Do you mean B' is the complement or?

5/8= 2/5 + P(B) -p(B)2/5
so P(B)=9/56 Could you tell me how yo u got this?
4. (Original post by Jonario)
5/8= 2/5 + P(B) -p(B)2/5
so P(B)=9/56 Could you tell me how yo u got this?
By making a mistake

Actually I think all you have to do is just note P(omega)=1 thus 1=P(C) +P(A) +P(B) thought this would give you 4/15. Sorry about that, its too late for me.

For the second question:

P(B)= 2/3 - 1/2
PA|B)=P(AnB)/P(B)=P(A) (as independent)
P(B|A)= P(BnA)/P(A)=p(B) as independent
5. (Original post by zcomputer5)
By making a mistake

Actually I think all you have to do is just note P(omega)=1 thus 1=P(C) +P(A) +P(B) thought this would give you 4/15. Sorry about that, its too late for me.
6. (Original post by Jonario)
4/15

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: December 7, 2010
Today on TSR

### Oxford or Cambridge?

I just can't decide

### Should I move back home?

Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

## Groups associated with this forum:

View associated groups
Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.