Housing project You are assigned the task of developing a new urban housing proj

Question

Housing project You are assigned the task of developing a new urban housing project in the Queens borough. Your responsibilities include an overall assessment of the structural mechanics of the material that will be used in the project, transportation facility, energy efficiency of the buildings and the overall safety factors and design aspects. The anticipated time of completion for the project is 3 years. However, this is conditional on having good weather for at least 2 years continuously. If in any given year there are three possibilities of the weather good, (G) normal (N) and bad (B), what is the probability that the housing project will be completed in the anticipated 3-year time? Assume each years weather is independent of any other year and the different weather conditions have the same probability in each year.

Explanation / Answer

as probability of having good ; normal and bad are all equal ; therefore probability of having a good weather =1/3

and probability of not good weather =1-1/3 =2/3

hence probability of having completed the project in 3 years =P(having good weather in first and second year+havning not good weather in first year and having good weather in 2nd and 3rd year)

=(1/3)*(1/3)+(2/3)*(1/3)*(1/3) =5/27

please revert for any clarification rquired (if not continuous this probability will be 7/27)

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