Simple probabilities

WARNING RED is only for dyed in the wool mathematicians.

1. Distribution of opponents cards cf. also the missing cards calculator

a.       If you are declarer and have 11 cards of a suit, what is the chance, the suit is divided 1/1 in the opponents hands?
Combin(2;1)*Combin(24;12)/combin(26;13) = 52%
To verify type in the missing cards calculator: xx and get 24% 52% and 24%

a.       If you are declarer and have 10 cards of a suit, what is the chance, the suit is divided 2/1 in the opponents hands?
Combin(3;1)*Combin(23;12)/combin(26;13) = 39%  is the chance for 1-2.
The same for 2-1 sums up to 78%
To verify type in the missing cards calculator: xxx and get 11% 39% 39% and 11%

2. Rolling dices

a.       Rolling a dice, what is the chance to hit a 6? 1 out of 6 = 1/6 = 16,7%

b.      Rolling a dice what is the chance to get a number which is greater than 2?
4 out of 6 = 4/6 = 66,7%

c.       Rolling 2 dices, what is the chance getting exactly 7 points?
1+6=7  2+5=7  3+4=7  4+3=7  5+2=7  6+1=7
6 out of 36 = 6/36 = 1/6 = 16,7%

3. Bridge hands:

a.       How many different hands of 13 out of 52 cards are possible? Combin(52;13)= 635.013.559.600

b.      What is the chance, to hold exactly 0, 1, 2, 3 or 4 aces in your hand?
0 Aces:     combin(4;0)*combin(48;13)/combin(52;13)=         30,38%
1 Ace:      combin(4;1)*combin(48;12)/combin(52;13)=          43,88%
2 Aces:     combin(4;2)*combin(48;11)/combin(52;13)=          21,35%
3 Aces:     combin(4;3)*combin(48;10)/combin(52;13)=          4,12%
4 Aces:     combin(4;4)*combin(48;9)/combin(52;13)=            0,26%