Book: Introduction to probability & statistics 13th edition Author: Mendenhall,

Question

Book: Introduction to probability & statistics 13th edition
Author: Mendenhall, Beaver, Beaver.

Q: 5.77
During the 1992 football season, the Los Angeles Rams (now the St.louis Rams) had a bizarre streak of coin-toss losses. In fact, they lost the call 11 weeks in a row.

a. The Rams' computer system manager said the odds against losing 11 straight tosses are 2047 to 1. Is he correct? (Answer: yes)

b. After these results were published, the Rams lost the call for the next two games, for a total of 13 straight losses. What is the probability of this happening if, in fact, the coin was fair? (Answer: 1/8192=.00012)

Please explain how they got these answers.

Explanation / Answer

a)
The total number of exhaustive cases is 2^11=2048. Yes, it is correct that the odds against losing 11 straight tosses are 2047 to 1.
b) The coin was fair, the total number of exhaustive cases is 2^13=8192. So, the probability of this happening is 1/8192=0.00012.

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