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Word Problem for probability ratio

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It is said that Napoleon assessed probabilities at the battle of waterloo in 1815. his hopes for victory depended on keeping the English and Prussian armies seperated. Believing that they had not joined forces on the morning of the fateful battle, he indicated his belief that he had a 90% chance of defeating the English; P(Napoleon wins) = .90

When told later that elements of the Prussian force had joined the English, Napoleon revised his opinion downward on the basis of this information, but his posterior probability was still 60%;
P(Napoleon Wins|Prussian and English Join forces) = .60

Suppose Napoleon were using Bayes' theorm to revise his information. To do so, he would have had to make some judgements about P(Prussian and English Join forces |Napoleon Wins) and P(Prussian and English Join forces |Napoleon loses). In particular, he would have had to judge the ratio of these two probabilities.

Based on the prior and posterior probabilities given above, what is that ratio?

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Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
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