You are about to start playing matches of a video game, but you cannot play all night because you must study for your exam tomorrow. Suppose the probability of winning each match with probability 0.8 and the outcome of each match is independent. You tell yourself that you will stop playing and start studying after losing 3 matches. What is the probability that you play at most 10 matches?

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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You are about to start playing matches of a video game, but you cannot play all night because you must study for your exam tomorrow. Suppose the probability of winning each match with probability 0.8 and the outcome of each match is independent. You tell yourself that you will stop playing and start studying after losing 3 matches. What is the probability that you play at most 10 matches?

Hint: Use the negative binomial distribution. You need to define a random variable.

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