IIT JEE , AIEEE Forum - Mathematics , Algebra

kishan12

A draw two cards at random from a pack of 52 cards.After returning them to the pack and shuffling it,B draws two cards at random.The probability that there is exactly one common card is..................
Ans is 50/663

Plzzz explain every step.Good explained ans will be given a minimum of 5 SALUTES.....for sure..

kuttan

let the cerds 'A' got be x and y;
to find probability of getting atleast any one of x or y;

ie,Required probability=
probability of getting x common OR y common OR both x & y;

P(getting x common)=
P(getting x in 1st draw)+P(getting xin 2nd draw);
=1/52+1/51
=103/2652;
similarly getting y common=103/2652;

getting both common=2/C(52,2);
=4/2652;

So, Probability=(103+103+4)/2652
=210/2652
=105/1326

Werewolf

Suppose A takes out cards named x and y
Now its B's turn , he has to take out card x in his first draw and any other card in his next draw except card y . This has probability 1/52*50/51 and since he can take out other card first and card x in second draw so his probability is 1/52*50/51*2

Now also we can repeat the same solution for card y which again has probability 1/52*50/51*2

Adding the two probabilities we get 1/52*50/51*2 + 1/52*50/51*2 = 50/663

sboosy

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