, Beschrijvende Statistieken en
Kansrekening
1 Kansenrekening
Voorbeeld: Trek een kaart
Events:
A = aas
Ā= geen aas (complement van aas)
B = zwart
B̄ = rood (complement van zwart)
B B̄
A 2 2 4
Ā 24 24 48
26 26 52
• P (A) = 4/52 = 1/13
• P (B) = 26/52 = 1/2
• P (Ā) = 1 − P (A) = 12/13
EN
z}|{
• P (A ∩ B) = 2/52 Opmerking: P (A ∩ B) = P (B ∩ A)
EN/OF
z}|{
• P (A ∪ B) = P (A) + P (B) − P (A ∩ B) Opmerking: P (A ∪ B) = P (B ∪ A)
= 4/52 + 26/52 − 2/52 = 28/52
• ’Conditional Probability’:
gegeven
z}|{
P (A | B) = 2/26 ’intuitief ’
P (A ∩ B) 2/52
P (A|B) = = 26/52 = 2/26 Opmerking: P (A|B) 6= P (B|A)
P (B)
• Events zijn onafhankelijk als geldt:
P (A|B) = P (A)
of (equivalent)
P (A ∩ B) = P (A) × P (B)
In het Vb:
P (A ∩ B) = 2/52
P (A) × P (B) = 4/52 × 1/2 = 2/52
Dus P (A ∩ B) = P (A) × P (B) en dus zijn A en B onafhankelijk.
• Twee events K en L zijn mutually exclusive als geldt: P (K ∩ L) = 0
In het Vb:
P (A ∩ Ā) = 0
Dus A en Ā zijn mutually exhaustive.
3 STATUU
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