Five women are playing poker. After being dealt five cards each, the women are
holding a total of eight diamonds and six spades.
The women have 5*5=25 cards altogether.
8 of those are diamonds,
6 of those are spades,
and therefore the remaining 25-(8+6)=25-14=11 in their hands
are hearts and clubs.
Since they have 25 cards already, there are 52-25=27 cards left
in the deck. They consist of the remaining 13-8=5 diamonds,
the remaining 13-6=7 spades, and the rest hearts and clubs.
1. What is the probability that the next card dealt will be a diamond?
5 diamonds out of 27 cards = 
2. What is the probability that the next two cards dealt will be spades?
The probability of the first card dealt being a spade is 7 spades out of 27
cards or 
. Then the probability of the second card being a spade is
6 spades out of 26 cards or 
which reduces to 
. So the probability
of the first AND the second cards both being spades is their product =
which reduces to 
.
Edwin
