Bonjour,
1) Le tirage se fait sans remise.
Après le premier tirage (jeton rouge), il reste 23 jetons: 9 jetons rouges, 8 verts et 6 bleus.
[tex]P_{R1}[/tex](R2) = 9/23
2) Après le premier tirage (jeton rouge), il reste 23 jetons: 10 jetons rouges, 8 verts et 5 bleus.
[tex]P_{B1}[/tex](V2) = 8/23
3) [tex]P_{R1}[/tex](V2) = 8/23
[tex]P_{V1}[/tex](V2) = 7/23
[tex]P_{B1}[/tex](R2) = 10/23
4)
P(R1) = 10/24 = 5/12
---------- [tex]P_{R1}[/tex](R2) = 5/12 * 9/23 = 45/276 = 15/92
---------- [tex]P_{R1}[/tex](V2) = 5/12 * 8/23 = 40/276 = 10/69
---------- [tex]P_{R1}[/tex](B2) = 5/12 * 6/23 = 30/276 = 5/46
P(V1) = 8/24 = 1/3
---------- [tex]P_{V1}[/tex](R2) = 1/3 * 10/23 = 10/69
---------- [tex]P_{V1}[/tex](V2) = 1/3 * 7/23 = 7/69
---------- [tex]P_{V1}[/tex](B2) = 1/3 * 6/23 = 6/69 = 2/23
P(B1) = 6/24 = 1/4
---------- [tex]P_{B1}[/tex](R2) = 1/4 * 10/23 = 5/46
---------- [tex]P_{B1}[/tex](V2) = 1/4 * 8/23 = 2/23
---------- [tex]P_{B1}[/tex](B2) = 1/4 * 5/23 = 5/92
