Question 1136178

How many diamonds are there in a full deck? Call that {{{d}}}.
How many cards in the whole deck? Call it {{{c}}}.
 
the probability of the first card being a diamond is {{{d/c}}}.
 
after that diamond is drawn, how many diamonds are left in the deck? the answer is {{{(d-1)}}}.
how many cards are left in the deck? the answer is {{{(c-1)}}}.
 
the probability of of the second card being a diamond is{{{ (d-1)/(c-1)}}}
 
To get the probability of both, multiply the two fractions:

{{{d(d-1)/c(c-1)}}}

 standard {{{52}}}-deck of cards with four suits: hearts, clubs, diamonds, and spades; there are {{{13}}} cards per suit.

=>
{{{c=52}}}
{{{d=13}}}

so, the probability that two diamonds are drawn is:

{{{d(d-1)/c(c-1)=13(13-1)/52(52-1)=(13*12)/(52*51)=156/2652=0.0588235294117647=0.059}}}