Question

Two cards are drawn simultaneously from a normal pack of 52 cards . What is the probability that at least one of them is spade

Answer 1

Number of ways to draw 2 cards from a pack of 52 cards =

52

C

2

= 1326. Number of ways to draw 2 kings from 4 kings =

4

C

2

= 6. Therefore, required probability = 6/1326 = 1/221.

i hope this helps

#bebraily

Answer 2

[0010001111]... Hello User... [1001010101]
Here's your answer...

There are two possible cases when there is at least one spade.
Either both the cards must be spades or pnly one must be a spade and the other must be from a different suit.
The no. of ways for the first case is C(13, 2)
= 13! ÷ (2!×11!)
= 78
The no. of ways for the second case is C(13, 1) × C(39, 1)
= {13! ÷ (1!×12!)} × {39! ÷ (1!×38!)}
= 13×39
= 169×3
= 534
No. of favourable outcomes = 78+534 = 612
Total outcomes = C(52, 2) = 1326

P(E) = 612/1326
= 306/663
= 102/221
= 6/13

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//I may have made a calculation mistake, but the logic is correct