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maths question

PLEASE CAN ANY ONE HELP ME WITH THIS THIS QUESTION ITS VERY URGENT AND PLEASE COULD ANYONE POST CALCULATIONS WITH A FINAL ANSWER WOULD BE GREATLY APPRECIATED.
Q3) A coffeeshop has 14 students in it. Of these 14 students, 10 are from the Economics department. One of the students leaves and goes to the library. The library had 25 students in it, not including the one who just came in. Of these 25, 5 are Economics students. After half an hour, a student leaves the library and goes back towards the coffee shop. What is the probability that this person is an Economics student?

Reply 1

username2116415

Wow, this is more an exercise in reading

ok, so we know

Coffee shop:
Ec - 10
other - 4

Library
Ec - 5
other - 20

There are 4 scenarios from here

*Economics goes to library, Economics walks back
*Economics goes to library, Non-Ec comes back
*Non-ec goes to library, Ec comes back
*Non-ec goes to library, Non-ec comes back

I'll use E to denote Economics going to library, and F to denote Economics coming back

P(E) =10/14 = 5/7
P(¬E) = 4/14 = 2/7
P(F) is dependant on E

P(F|E) = 6/20 = 3/10 (as one has appeared from coffee)
P(F|¬E) = 5/20

=> P(F) = 11/20
Someone call me out if i've been an idiot.