probability

Question

Two cards are drawn from a pack of well shuffled deck of 52 cards one after the other withour replacement.The probability of first card being a spade and second a black king is

(1) 1/104

(2) 3/338

(3) 25/2652

(4) 26/2652

Comments

C] 25/2652 ?

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yes, its C

Answer 1

there are two case the first black spade is king or not

case1: when it is king so probability will be 1/52 * 1/51

there will be 2 black kings but one is spade so when one spade king is selected then the next attempt will have only one king left

case2: when it is not king so probability will be 12/52 * 2/ 51

here 13 spades will be there but one is king so 12 fav cases and next attempt we can take 1 king from 2 black kings available

so adding them both 25/2652 is the answer

Comments

Case 1:

How 1/52 * 1/51?

Why not 13/52 * 1/51 (As in the first attempt we are selecting spades which are 13 in numbers.

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1/51 (the probability of selecting black spade king card) * 1/51 (selecting second black king)