Description
this is a probability hw
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Explanation & Answer
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Running head: MATH 331
Math 331
Homework 2
Instructor: Dr. Brown
MATH 331
2
1. We roll a fair die repeatedly until we see the number four appear and then we stop.
a) Following the example discussed in class, describe a sample space Ω and a
probability measure P to model this situation.
Solution
Modelling the outcomes of the experiment as the number of times we rolled the
die we take Ω={∞, 1,2,3,…}.
For k≥ 1, we have:
P(k)=P{needed k rolls}=P{no fours in the first k-1 rolls, then a 4}.
Counting the number of ways we cannot roll a four on each roll (5), we have
5
1
P(k)=P{no fours in the first k-1 rolls, then a 4}= ( )𝑘�...