Question

Determinati probabilitatea ca alegand la intamplare o pereche (x,y) din produsul cartezian MxM, sa avem x+y=5. 

Answer 1

Perechile de numere naturale care verifica egalitatea x+y=5 sunt: (0,5);(1,4);(2,3);(3,2); (4,1);(5,0). Avem in total 6 perechi.
Multimea M este fomata din elementele 0,1,2,3,4,5. M={0,1,2,3,4,5}
Produsul cartezian MxM={(0,0),(0,1),...,(0,5),----6 perechi
(1,0),(1,1),..(1,5),----6 perechi
(2,0),(2,1),..(2,5),----6 perechi
(3,0),(3,1),..(3,5),----6 perechi
(4,0),(4,1),..(4,5),----6 perechi
(5,0),(5,1),..(5,5),----6 perechi }
In concluzie, produsul cartezian MxM are 36 de elemente.
$p= \frac{6}{36}= \frac{1}{6}$