Search 72,432 tutors FIND TUTORS
Search for tutors
Ask a question
0 0

You draw three cards from a standard deck without replacement.

Tutors, please sign in to answer this question.

1 Answer

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