Question

Prawdopodobieństwo
Zadania są w załączniku

Answer 1

1.
|Ω|=6²=36
a)
A={5}×{1,2,3,4,6}U{1,2,3,4,6}×{5}
|A|=1∙5+5∙1=10
P(A)=|A|/|Ω| = 10/36=5/18

b)
B={1,2,3,4,5,6}×{1,2,3,4,5,6} / {2,3,4,5,6}×{2,3,4,5,6}
|B|=6∙6-5∙5=36-25=11
P(B)=|B|/|Ω| = 11/36

2.
6+5+4=15
|Ω|=15∙14∙13=2730
|A|=6∙5∙4=120
P(A)=|A|/|Ω| = 120/2730=4/91

3.
|Ω|=(40 5) = 40!/(35! 5!)=36∙37∙38∙39∙40/(1∙2∙3∙4∙5)
|A|=(39 4) = 39!/(35! 4!)=36∙37∙38∙39/(1∙2∙3∙4)
P(A)=|A|/|Ω| = (36∙37∙38∙39)/(1∙2∙3∙4) ∙(1∙2∙3∙4∙5) /(36∙37∙38∙39∙40) = 5/40 = 1/8

4.
Wystarczy tutaj przyjąć losowanie jednej karty:
|Ω|=52
|A|=4
P(A)=|A|/|Ω|=4/52=1/13

5.
|Ω|=6³=216
A={(1,1,1),...,(1,1,6),(1,2,1),...,(1,2,6),(1,3,1),...,(1,3,5),(1,4,1),...,(1,4,4),(1,5,1),...,(1,5,3),(1,6,1),(1,6,2) , (2,1,1),...,(2,1,6),(2,2,1),...,(2,2,5),......,(6,1,1),(6,1,2),(6,2,1)}
|A|=6+6+5+4+3+2  + 6+5+4+3+2+1 + 5+4+3+2+1  + 4+3+2+1  +3+2+1 +2+1
=81
P(A)=|A|/|Ω|=81/216 = 3/8

6.
P(A)=5/(5+3) = 5/8
P(B)=6/(6+2) = 6/8
P(C)= 1/2 P(A)+1/2 P(B) = 5/16+6/16=11/16