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Example 1. A coin is tossed three times. A uniform sample space for this problem contains eight points, hhh hht hth ttt tht (2.3) thh tth htt and we attach probability to each. Now let us use this sample space to answer some questions. What is the probability of at least two tails in succession? By actual count, we see that there are three such cases, so the probability is What is the probability that two consecutive coins fall the same? Again by actual count, this is true in six cases, so the probability is or . If we know that there was at least one tail, what is the probability of all tails? The point hhh is now ruled out; we have a new sample space consisting of seven points. Since the new information (at least one tail) tells us nothing new about these seven outcomes, we consider them equally probable, each with probability . Thus the probability of all tails when all heads is ruled out is . (See problems 11 and 12 for further discussion of this example.)

Example 1. A coin is tossed three times. A uniform sample space for this problem contains eight points, hhh hht hth ttt tht (2.3) thh tth htt and we attach probability to each. Now let us use this sample space to answer some questions. What is the probability of at least two tails in succession? By actual count, we see that there are three such cases, so the probability is What is the probability that two consecutive coins fall the same? Again by actual count, this is true in six cases, so the probability is or . If we know that there was at least one tail, what is the probability of all tails? The point hhh is now ruled out; we have a new sample space consisting of seven points. Since the new information (at least one tail) tells us nothing new about these seven outcomes, we consider them equally probable, each with probability . Thus the probability of all tails when all heads is ruled out is . (See problems 11 and 12 for further discussion of this example.)

A First Course in Probability (10th Edition)
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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Example 1. A coin is tossed three times. A uniform sample space for this problem contains eight points, hhh hht hth ttt tht (2.3) thh tth htt and we attach probability to each. Now let us use this sample space to answer some questions. What is the probability of at least two tails in succession? By actual count, we see that there are three such cases, so the probability is What is the probability that two consecutive coins fall the same? Again by actual count, this is true in six cases, so the probability is or . If we know that there was at least one tail, what is the probability of all tails? The point hhh is now ruled out; we have a new sample space consisting of seven points. Since the new information (at least one tail) tells us nothing new about these seven outcomes, we consider them equally probable, each with probability . Thus the probability of all tails when all heads is ruled out is . (See problems 11 and 12 for further discussion of this example.)
Transcribed Image Text:Example 1. A coin is tossed three times. A uniform sample space for this problem contains eight points, hhh hht hth ttt tht (2.3) thh tth htt and we attach probability to each. Now let us use this sample space to answer some questions. What is the probability of at least two tails in succession? By actual count, we see that there are three such cases, so the probability is What is the probability that two consecutive coins fall the same? Again by actual count, this is true in six cases, so the probability is or . If we know that there was at least one tail, what is the probability of all tails? The point hhh is now ruled out; we have a new sample space consisting of seven points. Since the new information (at least one tail) tells us nothing new about these seven outcomes, we consider them equally probable, each with probability . Thus the probability of all tails when all heads is ruled out is . (See problems 11 and 12 for further discussion of this example.)
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