From f03b2f31add52cb4726b7b64d09e1e0466df39e7 Mon Sep 17 00:00:00 2001
From: Julian T <julian@jtle.dk>
Date: Tue, 9 Feb 2021 11:53:14 +0100
Subject: Add notes and assignments for prob m2

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 sem6/prob/m2/opgaver.md | 53 +++++++++++++++++++++++++++++++++++++++++++++++++
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+# Opgaver til prob m2
+
+## Opgave 1
+
+Man kan sige at chances for at en kvinde kommer først er 50%.
+
+$$
+P(1) = \frac 1 2
+$$
+
+Herefter kræver det at en mand for først og en kvinde får næste.
+
+$$
+P(2) = \frac 5 10 \cdot \frac 5 9 \\
+P(3) = \frac 5 10 \cdot \frac 4 9 \frac 5 8 \\
+P(4) = \frac 5 10 \cdot \frac 4 9 \frac 3 8 \cdot \frac 5 8
+$$
+
+osv.
+
+## Opgave 2
+
+### A)
+
+Dette har jeg gjort på papir.
+
+### B)
+
+$$
+P\left(X > \frac 1 2\right) = 1 - F\left(\frac 1 2\right) = 1 - \frac 1 4 = \frac 3 4
+$$
+
+### C)
+
+$$
+P(2 < X \leq 4) = F(4) - F(2) = 1 - \frac {11} {12} = \frac 1 {12}
+$$
+
+### D)
+
+$$
+P(X < 3) = \frac {11}{12}
+$$
+
+### E)
+
+$$
+P(X = 1) = \frac 2 3 - \frac 1 2 = \frac 1 6
+$$
+
+## Opgave 3
+
+
-- 
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