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There is a 10% chance that it won’t snow all winter long. There is a 20% chance that schools will not be closed all winter long. What is the greatest possible probability that it will snow and schools will be closed during the winter?
- a)55%
- b)60%
- c)70%
- d)72%
- e)80%
Correct answer is option 'E'. Can you explain this answer?
Verified Answer
There is a 10% chance that it won’t snow all winter long. There ...
There is a strong temptation to solve this problem by simply finding the probability that it will snow (90%) and the probability that schools will be closed (80%) and multiplying these two probabilties. This approach would yield the incorrect answer (72%), choice D. However, it is only possible to multiply probabilities of separate events if you know that they are independent from each other. This fact is not provided in the problem. In fact, we would assume that school being closed and snow are, at least to some extent, dependent on each other. However, they are not entirely dependent on each other; it is possible for either one to happen without the other. Therefore, there is an unknown degree of dependence; hence there is a range of possible probabilities, depending on to what extent the events are dependent on each other. Set up a matrix as shown below. Fill in the probability that schools will not be closed and the probability that there will be no snow.
Then use subtraction to fill in the probability that schools will be closed and the probability that there will be snow.
To find the greatest possible probability that schools will be closed and it will snow, fill in the remaining cells with the largest possible number in the upper left cell.
The greatest possible probability that schools will be closed and it will snow is 80%.
Then use subtraction to fill in the probability that schools will be closed and the probability that there will be snow.
To find the greatest possible probability that schools will be closed and it will snow, fill in the remaining cells with the largest possible number in the upper left cell.
The greatest possible probability that schools will be closed and it will snow is 80%.
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There is a 10% chance that it won’t snow all winter long. There ...
Calculating the Probability of Snow and School Closure
There is a 10% chance that it won’t snow all winter long. This means there is a 90% chance that it will snow during the winter.
There is a 20% chance that schools will not be closed all winter long. This means there is an 80% chance that schools will be closed during the winter.
Finding the Greatest Possible Probability
To find the greatest possible probability that it will snow and schools will be closed during the winter, we multiply the probabilities of each event happening.
Probability of snow = 90%
Probability of school closure = 80%
Therefore, the greatest possible probability that it will snow and schools will be closed during the winter is 90% x 80% = 72%.
Therefore, the correct answer is option E) 80%.
There is a 10% chance that it won’t snow all winter long. This means there is a 90% chance that it will snow during the winter.
There is a 20% chance that schools will not be closed all winter long. This means there is an 80% chance that schools will be closed during the winter.
Finding the Greatest Possible Probability
To find the greatest possible probability that it will snow and schools will be closed during the winter, we multiply the probabilities of each event happening.
Probability of snow = 90%
Probability of school closure = 80%
Therefore, the greatest possible probability that it will snow and schools will be closed during the winter is 90% x 80% = 72%.
Therefore, the correct answer is option E) 80%.
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