IIITH-PGEE 2017

Question

Consider 3 card one having both side painted red another having both side printed black and last having one side black and another side red, 3 cards are put in a hat and are mixed properly, now one card in picked and put down on table, its face up color is red what is probability that another side will be black.

Comments

From where do you get the questions ?

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I appeared for exam and based on my finest memory I wrote this down

Answer 1

Conditional Probability :  similar question

https://gateoverflow.in/41499/gate2014-ec01-ga10?show=41499#q41499

Answer : 1/3

Comments

P(both face black) = P(both face red) = P(one face red one face black) = 1/3

Question asked -

P(Second side is Black | First side is Red)  =  P(B,R) / P(R)

Now,

P(B,R) = P(Selecting card with one face Red and one face Black) * P(R|B)  = (1/3) *(1/2) = 1/6

P(R) = P(both face Red) * 1 + P(one face Red one face Black) * 1/2  

       = (1/3)*1 + (1/3) *(1/2) = 1/2

Thus , P(B|R) = (1/6) / (1/2) = 1/3

(Baye's Theorem)