five cards are selected from a fair deck. what is the possibility that they contain at least four spades?

Question

five cards are selected from a fair deck. what is the possibility that they contain at least four spades?

Answer 1

There are 52 cards total. 1/4 or 13 of the cards are spades. So of the 5 cards drawn, at least 4 is 4 or 5 spades. We can use the formula for sampling g good elements and b bad elements without replacing. This is GCg * BCb / NCn.

So 13C4* 39C1 / 52C5 + 13C5/52C5 =. 0107 +. 0005 =. 0112. You can look for the probability of 4 of a kind + probability of a flush in poker and divide by 4 (since it we are only allowed spades) and it will be very close.