x Turn on thread page Beta
 You are Here: Home >< Maths

# S1 - Probability help needed! watch

1. A garage sells three types of fuel; U95, U98 and diesel. In a survey of 200 motorists buying fuel at the garage, 80 are female and the rest are male. Of the 90 motorists buying ‘U95’ fuel, 50 were female and of the 70 motorists buying diesel, 60 were male. A motorist does not buy more than one type of fuel.

Find the probability that a randomly chosen motorist

b) is male, given that the motorist buys U98 fuel.

Garage records indicate that 10% of the motorists buying U95 fuel, 30% of the motorists buying U98 fuel and 40% of the motorists buying diesel have their car serviced by the garage.

A motorist is chosen at random.

c) Find the probability that this motorist has his or her car serviced by the garage.

d) Given the motorist has his or her car serviced by the garage, find the probability that the motorist buys diesel fuel.

I have answered questions part A-C. I am stuck on the last part- D.

Thanks!
2. (Original post by Jaydude)
A garage sells three types of fuel; U95, U98 and diesel. In a survey of 200 motorists buying fuel at the garage, 80 are female and the rest are male. Of the 90 motorists buying ‘U95’ fuel, 50 were female and of the 70 motorists buying diesel, 60 were male. A motorist does not buy more than one type of fuel.

Find the probability that a randomly chosen motorist

a) buys U98 fuel, I know this one.

b) is male, given that the motorist buys U98 fuel.

Garage records indicate that 10% of the motorists buying U95 fuel, 30% of the motorists buying U98 fuel and 40% of the motorists buying diesel have their car serviced by the garage.

A motorist is chosen at random.

c) Find the probability that this motorist has his or her car serviced by the garage.

d) Given the motorist has his or her car serviced by the garage, find the probability that the motorist buys diesel fuel.

I have answered questions part A-C. I am stuck on the last part- D.

Thanks!
Using your answer to part c) d) is just the P(A|B) where P(A) is the probability that a motorist buys diesel fuel and P(B) is the probability that the motorist has his or her car serviced by the garage.

Conditional Probability:- P(A|B) = P(A and B) / P(B)
3. (Original post by Black_Materia_)
Using your answer to part c) d) is just the P(A|B) where P(A) is the probability that a motorist buys diesel fuel and P(B) is the probability that the motorist has his or her car serviced by the garage.

Conditional Probability:- P(A|B) = P(A and B) / P(B)
Yep got to that, P(B)=0.245, however i cannot work out what P(AnB) is...

They say 40 perecent are likely to get it serviced for diesel,
40% of 70 =28.

So i tried P(AnB) = 28/70, but when i sub it into the equation P(A|B) = P(A and B) / P(B), it is Not Correct!

Can you help me figure out where I am going wrong?
4. Bump. Anyone?
5. Out of the 9+12+28 = 49 people who have service

So 28/49

I see why it is 28/49, however when i do P(A|B) = 28/49 divided by 0.245, i still got the wrong answer. I think I am making a simple mistake somewhere...
7. (Original post by Jaydude)

I see why it is 28/49, however when i do P(A|B) = 28/49 divided by 0.245, i still got the wrong answer. I think I am making a simple mistake somewhere...
Why are you dividing by 0.245

28/200 divided by 49/200 = 28/49
8. (Original post by Jaydude)

I see why it is 28/49, however when i do P(A|B) = 28/49 divided by 0.245, i still got the wrong answer. I think I am making a simple mistake somewhere...
P(A) = probability buying diesel fuel = 28 people (40% of 70 that buy diesel)
P(B) = probability serviced at garage = 49 (from part c)

P (A|B) = 28/49.
9. I see, so P(AnB) = 28/200. Problem solved! Thank you to those that helped out!
10. (Original post by Jaydude)
I see, so P(AnB) = 28/200. Problem solved! Thank you to those that helped out!
Hey, I know this is really late, but if anyone could tell me how to calculate parts B and C I'd be so grateful!!

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: November 30, 2016
Today on TSR

### Four things top students are doing

Over the Easter break

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