Question

In: Statistics and Probability

In Montana, the probability it will snow tomorrow is .55. The weather forecast correctly says that...

In Montana, the probability it will snow tomorrow is .55. The weather forecast correctly says that it will snow tomorrow when it will actually snow tomorrow with probability .9. The weather forecast also correctly predicts it will not snow tomorrow when it actually will not snow tomorrow with probability .95. Use a tree diagram to calculate the following questions:

What is the probability that the weather forecast says that it will snow tomorrow AND it actually will snow tomorrow?

What is the probability that the weather forecast says that it will snow tomorrow?

What the probability that it will snow tomorrow in Montana, given that the weather forecast says it will snow tomorrow.

What the probability that it will NOT snow tomorrow in Montana, given that the weather forecast says it will NOT snow tomorrow.

What the probability that it will snow tomorrow in Montana, given that the weather forecast says it will NOT snow tomorrow.

Solutions

Expert Solution

a) the probability that the weather forecast says that it will snow tomorrow AND it actually will snow tomorrow = 0.9*0.55 = 0.495

b) the probability that the weather forecast says that it will snow tomorrow = 0.9*0.55+0.05*0.45 = 0.5175

c) the probability that it will snow tomorrow in Montana, given that the weather forecast says it will snow tomorrow = 0.495/0.5175 = 0.9565

d) the probability that it will NOT snow tomorrow in Montana, given that the weather forecast says it will NOT snow tomorrow = ( 0.95*0.45)/(0.95*0.45+0.55*0.1) = 0.886

e) the probability that it will snow tomorrow in Montana, given that the weather forecast says it will NOT snow tomorrow = 0.1*0.55/(0.1*0.55+0.95*0.45) = 0.114

orchestra answered 2 years ago
Next > < Previous

Related Solutions

the probability that the weather will be cold on sunday is .75 if the weather is...
the probability that the weather will be cold on sunday is .75 if the weather is cold there is a probability of 0.30 that barney wins if the weather is not cold there is a probablity of 0.90 that fred will win what is the probability the weather is cold and fred wins what is the probability the weather is not cold and barney wins
the probability that the weather will be cold on sunday is .75 if the weather is...
the probability that the weather will be cold on sunday is .75 if the weather is cold there is a probability of 0.30 that barney wins if the weather is not cold there is a probablity of 0.90 that fred will win what is the probability barney wins the match fred wins the match
Price Today, A Price Today, B State Tomorrow Probability Price Tomorrow, A Price Tomorrow, B 30...
Price Today, A Price Today, B State Tomorrow Probability Price Tomorrow, A Price Tomorrow, B 30 20 Good 0.5 60 40 Bad 0.5 15 5 1a). Given the following information, calculate the correlation coefficient between the returns on stocks A and B a. 0 b. 0.25 c. 0.5 d. 0.75 e. 1 1b). Calculate expected return and standard deviation of the portfolio that is allocated 40% to A, 60% to B.
10. Weather forecast : athe table below indicates the accuracy of a local weather report with...
10. Weather forecast : athe table below indicates the accuracy of a local weather report with respect to rain or no rain over the past year. This table gives the results of 365 consecutive days and compares whether it rained or not to whether or not rain was predicted. Did it actually rain? yes No Report predicted Rain 102 18 Report predicted No Rain 40 205 If one day is randomly selected from these 365 days, what is the probability...
Suppose that the chance of rain tomorrow depends on previous weather conditions only through whether or...
Suppose that the chance of rain tomorrow depends on previous weather conditions only through whether or not it is raining today and not on past weather conditions. Suppose also that if it rains today, then it will rain tomorrow with probability 0.6, and if it does not rain today, then it will rain tomorrow with probability 0.3, then a. Calculate the probability that it will rain four days from today given that it is raining today. b. What is the...
Write a class encapsulating the concept of the weather forecast, assuming that it has the following...
Write a class encapsulating the concept of the weather forecast, assuming that it has the following attributes: the temperature and the sky conditions (e.g. sunny, snowy, cloudy, rainy, etc.).  Include a default constructor, an overloaded constructor, accessors and mutators, and the methods, toString() and equals(). Temperature, in Fahrenheit, should be between -50 and +150; the default value is 70, if needed. The default sky condition is sunny. In Addition, include a method that converts Fahrenheit to Celsius. Celsius temperature = (Fahrenheit...
STATE OF WEATHER PROBABILITY OF STATE OF WEATHER INVESTMENT AND LIKELY RETURNS Pig Farming Crop Farming...
STATE OF WEATHER PROBABILITY OF STATE OF WEATHER INVESTMENT AND LIKELY RETURNS Pig Farming Crop Farming Floriculture BAD 20% 2% -3% -5% GOOD 50% 10% 7% 11% EXCELLENT 30% 20% 15% 25% INVESTMENT N$ 300, 000 250, 000 450, 000 Required: a. Calculate the farmer’s Expected return on the floriculture investment. b. What is the Standard Deviation of the pig farming project? c. What is the farmer's Expected combined return if he invests in the three farming activities as shown...
The weather report says the temperature is 78.0°F, the barometer is at 29.90 inches Hg, the...
The weather report says the temperature is 78.0°F, the barometer is at 29.90 inches Hg, the relative humidity is 67.0%. Estimate the mole fraction of water in the air, the molal humidity, absolute humidity, percentage humidity in the air, and the dew point a) What is the mole fraction of water in the atmosphere? b) Determine the molal humidity.(mol H2O)/(mol dry air) c) Determine the absolute humidity.(g H2O) / (g dry air) d) Determine the percent humidity. e) What is...
Problem 3 Assume that the probability of rain tomorrow is 0.5 if it is raining today,...
Problem 3 Assume that the probability of rain tomorrow is 0.5 if it is raining today, and assume that the probability of its being clear (no rain) tomorrow is 0.9 if it is clear today. Also assume that these probabilities do not change if information is also provided about the weather before today. a) Find the n-step transition matrix for n = 3, 7, 10, 20. b) The probability of rain today is 0.5 Use the results in the part...
The weather forecast predicts an 80% chance of rain in the next hour. If rain follows...
The weather forecast predicts an 80% chance of rain in the next hour. If rain follows a poisson distri bution, what is the chance of rain in the next HALF hour? Comment on the difference between the probability of rain in the next half hour versus the next hour. Before doing a calculation, what do you expect your answer to be: Best guess for chance of rain in next half hour: Calculation:
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT