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Probability Based on Random Selection

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There are three boxes, each with two drawers.

Box I has a gold coin in each drawer
Box II has a silver coin in each drawer
Box III has a gold coin in one drawer and a silver coin in the other.

One box is chosen at random and a drawer is opened from that box. If it contains a gold coin, find the probability that it is in Box I.

Solution Summary

Probabilities based on random selection are calculated. Some knowledge of probability theory may be required to understand the solution.

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Solution. Denote the events that Box I, Box II and Box III are chosen by A, B and C, respectively. Then we know that ...

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• 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"
• "Thank you very much for your valuable time and assistance!"

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