Question

A weather forecast states that there is a 20% probability of rain in the next three days. Describe a simulation you could perform using random numbers to find the experimental probability that it will not rain on any of the next 3 days.

Answer 1

Answer:

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Step-by-step explanation:

Before leaving for work, Victor checks the weather report in order to decide whether to carry an umbrella. The forecast is “rain" with probability 20% and “no rain" with probability 80%. If the forecast is “rain", the probability of actually having rain on that day is 80%. On the other hand, if the forecast is “no rain", the probability of actually raining is 10%.

1. One day, Victor missed the forecast and it rained. What is the probability that the forecast was “rain"?

2. Victor misses the morning forecast with probability 0.2 on any day in the year. If he misses the forecast, Victor will flip a fair coin to decide whether to carry an umbrella. (We assume that the result of the coin flip is independent from the forecast and the weather.) On any day he sees the forecast, if it says “rain" he will always carry an umbrella, and if it says “no rain" he will not carry an umbrella. Let U be the event that “Victor is carrying an umbrella", and let N be the event that the forecast is “no rain". Are events U and N independent?

3. Victor is carrying an umbrella and it is not raining. What is the probability that he saw the forecast?