Let a coin have probability of heads p and probability of tails q ≜ 1−p, for some p ∈ (0, 1). The coin is flipped repeatedly. Derive an expression for the probability that a sequence of n consecutive heads occurs before a sequence of m consecutive tails, for given integers n ≥ 1 and m ≥ 1. The resulting expression involves p, q, m, n. Use your expression to compute the answer for p = 1/3, q = 2/3, n = 3, and m = 6.

Let a coin have probability of heads p and probability of tails q ≜ 1−p, for some p ∈ (0, 1). The coin is flipped repeatedly. Derive an expression for the probability that a sequence of n consecutive heads occurs before a sequence of m consecutive tails, for given integers n ≥ 1 and m ≥ 1. The resulting expression involves p, q, m, n. Use your expression to compute the answer for p = 1/3, q = 2/3, n = 3, and m = 6.

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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Question

Let a coin have probability of heads p and probability of tails q ≜ 1−p, for some p ∈ (0, 1). The
coin is flipped repeatedly. Derive an expression for the probability that a sequence of n consecutive heads
occurs before a sequence of m consecutive tails, for given integers n ≥ 1 and m ≥ 1. The resulting expression
involves p, q, m, n. Use your expression to compute the answer for p = 1/3, q = 2/3, n = 3, and m = 6.

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