Statistics Question

[PocketJokers72]

Flip up 5 cards out of a standard 52 card deck. The probability that at least 1 will be a spade?

Please show me HOW to do the math. I can do other things statistics-wise, but I'm whiffing big time on this one.

[Tom1975]

1 - (39/52)*(38/51)*(37*50)*(36/49)*(35/48)

[PocketJokers72]

OK...5 seperate decks. 1 card from each deck. 5 cards flipped up. The probability that AT LEAST 1 will be a spade?

[Tom1975]

1 - (39/52)^5

[PocketJokers72]

makes total sense...I guess I couldn't see the forest for the trees. TYVM.

[UATrewqaz]

This is a grunch

The odds of there being at LEAST 1 spade is easiest to calculate as follows

1.00 - the odds of there being NO spade.

The odds of there not being any spade is

39/52 * 38/51 * 37/50 * 36/49 * 35/48

which is ~ 22.15%

Thus the odds of there being at least one spade on the board is ~ 77.85%

(this goes for any suit of course)



(that is to say, the total number of boards without spades divided by the total number of boards period).