Probability question (mind has frozen)

[James Smithson]

I normaly understand probability and find it easy so I have no idea why I cant wrap my head around a question thats popped up.
First here is the table of data and below the table i will pop the question that I cant get my head around. Thank you in advance for any help.

Number of Archeology students

	2013	2014	2015	2016	2017	2018	2019	Total
Scotland	45	54	63	72	62	42	40	378
Other Area	250	297	303	316	423	355	520	2464
Total	295	351	366	388	485	397	560	2842

What is the probability that a randomly chosen Archaeology student studied in Scotland and/or studied Archaeology in 2018?


.....

this is confusing me.

The best I have come up with is work out the probability a student is scotish and work out a student studied in 2018 and then addthe probablitys but I am probably way out there .

If this is the case I end up with an answer of ≃ 0.148

Any help here I would be over the moon for.

Thank you for even replying it means a lot

 

[Dr.Peterson]

What is the probability that a randomly chosen Archaeology student studied in Scotland and/or studied Archaeology in 2018?

It's an odd question, since you have to assume that all archaeology students (ever?) did so in one of these years, and that you have a way of randomly choosing a (current or former) student.

But taking the question at face value, one can just add up all the students in either the Scotland row or the 2018 column. That can be done more quickly using the inclusion-exclusion formula for the probability of "or".

The best I have come up with is work out the probability a student is scotish and work out a student studied in 2018 and then addthe probablitys but I am probably way out there .

If this is the case I end up with an answer of ≃ 0.148

Please show the details of your calculation. I don't get that number even by doing what you say you did.

But it sounds like you are forgetting that you can only add mutually exclusive probabilities.

 

[James Smithson]

It's an odd question, since you have to assume that all archaeology students (ever?) did so in one of these years, and that you have a way of randomly choosing a (current or former) student.

But taking the question at face value, one can just add up all the students in either the Scotland row or the 2018 column. That can be done more quickly using the inclusion-exclusion formula for the probability of "or".

Please show the details of your calculation. I don't get that number even by doing what you say you did.

But it sounds like you are forgetting that you can only add mutually exclusive probabilities.

I think I messed up...

The probability of selecting a archeology student who studied in scotlandi in 2018 :
42/2842 ≃ 0.015
The probability of selcting a archeology student who studied in scotland :
378/2842 ≃ 0.133

i added 0.015 to 0.133 to get 0.148
if i multiply them is that the right way to go ? it comes out with a wierd number that i dont really understand i think it may translate to ≃ 0.002

 

[Dr.Peterson]

I think I messed up...

The probability of selecting a archeology student who studied in scotlandi in 2018 :
42/2842 ≃ 0.015
The probability of selcting a archeology student who studied in scotland :
378/2842 ≃ 0.133

i added 0.015 to 0.133 to get 0.148
if i multiply them is that the right way to go ? it comes out with a wierd number that i dont really understand i think it may translate to ≃ 0.002

Why would you add those two things, one of which is included in the other? And why in the world would you multiply them??

You are asked for "the probability that a randomly chosen Archaeology student studied in Scotland and/or studied Archaeology in 2018". The "and/or" represents the usual inclusive or. How do you find P(A or B)?

Here are the students they're asking about:

	2013	2014	2015	2016	2017	2018	2019	Total
Scotland	45	54	63	72	62	42	40	378
Other Area	250	297	303	316	423	355	520	2464
Total	295	351	366	388	485	397	560	2842

 

[James Smithson]

taken your advice taken some time and this is what I have now.

P(A or B) = P (A) + P (B) – P (A and B)

378/2842 + 397/2842 - 42/2842 = 733/2842 ≃ 0.258

feeling better about it I hope its right