Probability doubt

Question

A box contains 3 coins: two regular coins and one fake two headed P(H )= 1 .you pick up one at random and toss it and gets heads.the probability that it is a two headed coin is....

Answer 1

It is based on Bayes' Theorem.. 

Here it is given that head will occur..But we dont know if it will be due to the regular or fake coin..

P(regular coin)  =  2/3

P(fake coin)   =  1/3

P(head | regular coin)   =   1/2 [ As regular coin has one of two surfaces as head ]

P(head | fake coin)   =  1 [ As fake coin has both surfaces as head ]

Hence 

P(fake coin | head)    =    P(fake coin) * P(head | fake coin) /  [ (P(fake coin) * P(head | fake coin)) + (P(regular coin) * P(head | regular coin) )

                               =    1/3 * 1 /  [ 1/3 * 1 +  2/3 * 1/2 ]

                               =    1/2

Hence required probability   =   1/2

Comments

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