3 The anticipated time of completion for a housing project i

3. The anticipated time of completion for a housing project is 4 years. However, this is conditional on having good weather for atleast 3 years continuously. If there is a 50% chance of having good weather in any given year, what is the probability that the housing project will be completed in the anticipated 4-year time?

Solution

Given,

For the successful completion of the project within 4 years , we need three good weather years continously. And that there is 50% chance of having good weather in any given year.

So , There are only two possible ways in which the house can be completed successfully.

1. 1st year - Good Weather

2nd year - Good Weather

3rd year - Good Weather

4th year- Doesn\' matter as the house would already be constructed.

2. 1st year - Bad weather

2nd year -Good Weather

3rd year - Good Weather

4th year-Good Weather

These are the only two possible ways. We need to find the summation of these two possibilites

1) 1/2 (probability of good weather) * 1/2 (probability of good weather)* 1/2 (probability of good weather) = 1/8

2) 1/2 (probability of bad weather) * 1/2 (probability of good weather) * 1/2  (probability of good weather)* 1/2 (probability of good weather) = 1/ 16.

Hence total probability is (1/8) + (1/16) = 3/16.

Hence the probability that the housing project will be completed in the anticipated 4-year time is 3/16.

Let me know if you have doubts over this.