A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both diamonds. Find the probability of the lost card being a diamond.

Options

A. `11/50`
B. `13/50`
C. `17/50`
D. `19/50`

Answer

A

Explanation

let the event of lost card is diamond be A

let the event of both drawn card is diamond be B

`P(A)= 13/52 = 1/4`

`P'(A)= 1- 1/4 = 3/4`

`P(B/A)= 12/51*11/50`

`P(B/(A'))= 13/51* 12/50`

Now, `P(A/B)= (P(B/A).P(A))/(P(B/A).P(A) + P(B/A')P(A'))`

`= ((12*11)/(51*50)*1/4)/((12*11)/(51*50)*1/4 + (13*12)/(51*50)*3/4)`

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