You draw three cards from a standard deck without replacement.

Question

Determine the probability that none of the cards drawn is a Diamond.

Answer 1

Chris,

 

Probability is usually defined as the number of desired outcomes divided by the total number of possible outcomes.  In this case a deck of cards has 52 possible outcomes (1 for each card), 13 of which are diamonds or 52-13=39 not-diamonds, so the probability that I would draw a diamond on the first draw is 1/4 (13/52), and the probability that I do not draw a diamond is 3/4 (39/52).

 

So if I do not draw a diamond on the first draw (39/52) times, because there is no replacement, the odds that I do not draw a diamond again is 38/51; and again, after the second draw, the odds that I do not draw a diamond again is 37/50.  Because these are dependent events, we have to multiply these three numbers together.  Or (39*38*37)/(52*51*50). 

 

I hope this helps.  John