Question 352138
Hi,
*Note: exactly one card being a diamond: the other one chosen would not be a diamond.

The probability of a diamond being drawn is 1/4 or .25
The probability of a card not being a diamond is 3/4 or .75
.
The probability of x successes in n trials is: 
P = nCx* {{{p^x}}}*{{{q^(n-x)}}} where p and q are the probabilities of success and failure respectively. 
.
nCx = {{{n!/(x!(n-x)!)}}}
.

Of the two drawn(replacing the first), the probability of exactly one card of the two being a diamond is:
2C1 = {{{ 2!/(1!*0!)!= 1 }}}
.
P= {{{1*.25^1*.75^1}}} =.1875