The Trace household has triplets who have just turned 16, and all of them want to drive the family car to school. To determine who drives, they each toss a coin and the odd person gets to drive. If all coins show heads or tails, they toss again. What is the probability that a decision will be reached in four or fewer tosses?

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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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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The Trace household has triplets who have just turned 16, and all of them want to drive the family car to school. To determine who drives, they each toss a coin and the odd person gets to drive. If all coins show heads or tails, they toss again. What is the probability that a decision will be reached in four or fewer tosses?

Leekley, Robert M.. Applied Statistics for Business and Economics

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Step 1

For geometric distribution, there are four requirements need to be fulfilled. These requirements are mentioned below.

  • Each trial has only two possible outcomes (success or failure).
  • The probability of success/failure should remains constant for each trial.
  • The trials must be independent.
  • The variable of interest is the number of trials required to get first success.

Assume, X be the variable which follows the geometric distribution, representing the number of trials required to get first success, then the probability that PX=x, can be given as PX=x=1-px-1·p, where p be the success probability and x be the number of trials to get first success.

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