SOLUTION: Three cards are pulled from a deck of 52 cards. The probability of obtaining atleast one club is?

Question 1181538: Three cards are pulled from a deck of 52 cards. The probability of obtaining atleast one club is?
Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the probability of obtaining at least one club is 1 minus the probability of obtaining zero clubs.
there are 13 clubs in the deck.
that leaves 52 minus 13 = 39 cards in the deck that are not clubs.
if you assume no replacement, then the probability changes each time.
on the first draw, the probability of not drawing a club is 39/52.
on the second draw, the probability of not drawing a club is 38/51.
third draw = 37/50.
fourth draw = 36/49.
fifth draw = 35/48.
sixth draw = 34/47.
seventh draw = 33/46.
eighth draw = 32/45.
ninth draw = 31/44.
tenth draw = 30/43.
eleventh draw = 29/42.
twelth draw = 28/41.
thirteenth draw = 27/40
the probability of getting zero clubs is therefore equal to:
39/52 * 38/51 * 37/50 * 36/49 * 35/48 * 34/47 * 33/46 * 32/45 * 31/44 * 30/43 * 29/42 * 28/41 * 27/40 which is equal to:
(39*38*37*36*35*34*33*32*31*30*29*28*27) / (52*51*50*49*48*47*46*45*44*43*42*41*40)
which is equal to:
.012790948
the probability of getting at least one club is therefore 1 minus that which is equal to: .987209052.

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The method from the other tutor is fine -- but only three cards are being drawn....

P(at least on club) = 1-P(no clubs) = 1-((39/52)(38/51)(37/50))

You can do the calculation.

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