Probability question confusing me!

mikeystipey

Hi folks! I'm studying a probability question from a college past paper which I'm a little confused on. It goes as follows:

A survey of 100 students of means of transport to and from a secondary school reveals the following results:


Walk
Cycle
Driven
Other
Male
18
10
12
7
Female
22
6
16
9


(a) Demonstrate clearly how this data can be used to create a contingency table and show how it can be used to calculate the following probabilities, indicating and explaining whether these probabilities are examples of simple, joint or conditional probability:
(i) A male student is driven to school;
(ii) A student is female;
(iii) A student cycles to school given that the student is female.

So here's the contingency table, very easy:


Walk
Cycle
Driven
Other
Total
Male
18
10
12
7
47
Female
22
6
16
9
53
Total
40
16
28
16
100


Parts (ii) and (iii) are clear, they being simple and conditional probabilities respectively, and I know how to calculate them. However the wording of part (i) confuses me - is this a joint or a conditional probability?

I think its a conditional probability even though its not worded like that ('given that' etc.) I think the answer should be 12/47 = 0.26 probability.

However could this actually be a joint probability, just phrased badly. I think this because I think the examiner wanted to give an example of each tryp of probability in the 3 questions. If it is a joint probability I think it should be phrased as 'probability that a student is male AND is driven to school', in which case the answer would be 12/100 = 0.12 probability.

So is my probability flawed or is the question just phrased poorly? Would be very grateful for any help!

Mikey

mikeystipey

sorry, the contingency table didn't come out as I wished, here it is as an attachment

gerry87

I would understand it as a joint probability. 12/100

12/47 = probability that a student is driven to school, given that they're male.
12/28 = probability that a student is male, given that they're driven to school.
12/100 = probability that a male student is driven to work.

Use your table, or you can use bayesian:

P(A) = probability a student is driven to school = 28/100
P(B) = probability of male = 47/100
P(A|B) = probability that a student is driven to school, given that they're male. = 12/47
P(AB) = Probability a student is driven to school AND male. = ???

P(AB) = P(A|B)P(B)
P(AB) = (12/47)*(47/100) = 12/100

mikeystipey

Hi Gerry, thanks for your help! I would agree with you now actually, the wording of the question is just a bit confusing