40% chance it will rain 1 day and a 60% it will rain the next day. What is % it will rain 1 of the 2 days?

Answer 1

For the two days, the following probabilities can be found:
fair on first day = 0.6
rain on first day = 0.4
fair on second day = 0.4
rain on second day = 0.6

Combining these, we get 4 possibilities:
fair/fair: 0.6*0.4
fair/rain: 0.6*0.6
rain/fair: 0.4*0.4
rain/rain: 0.4*0.6

Now, just take the possibilities which meet the given conditions and add them together. The condition is that it rains 1 of the 2 days. It is not clear whether this means EXACTLY 1, or AT LEAST 1 of the 2 days; I will do both:

Chance that it will rain AT LEAST 1 of the 2 days:
rain/fair: 0.4*0.4 = 0.16
fair/rain: 0.6*0.6 = 0.36
rain/rain: 0.4*0.6 = 0.24
Total: 0.16 + 0.36 + 0.24 = 0.76 = 76%

Chance that it will rain EXACTLY 1 of the 2 days:
rain/fair: 0.4*0.4 = 0.16
fair/rain: 0.6*0.6 = 0.36
Total: 0.16 + 0.36 = 0.52 = 52%

Answer 2

I don't believe you can multiply the probabilities if that is what you are thinking. They are independent forecasts. There is a 40% probability that under the set of forecast conditions any point within the forecast area will have a 40% chance of receiving precip on day 1 and a 60% chance on day 2. The conditions for precip on the two days may be completely different.

Answer 3

50 % chance of rain in the next two days.

I don't see why they don't take the mean average of the 7 day forcast and say there is a certain % of rainfall in the next week. If it were 100%, we know the possibility of every day being 100% chance of rain, and if 70%, then there is a 70% chance of rain every day... But I guess we look for exactness, and want to know if we can expect rain every day.

Answer 4

50 percent