The chance we will have rain in 48 hours is the chance that it will rain
today AND/OR the chance that it will rain tomorrow. This can be
translated in 1 - chance that it will stay dry today AND it will stay
dry tomorrow, thus

P_some_rain_in_48_Hours = 1 - P_dry_today*P_dry_tomorrow.

P_dry_today = 1-P_rain_today = 1-0.5 = 0.5
P_dry_tomorrow = 1-P_rain_tomorrow=1-0.4=0.6
P_dry_today*P_dry_tomorrow = 0.5*0.6 = 0.3

The chance that we will have some rain in the next 48 hours thus becomes
P_some_rain_in_48_Hours = 1 - 0.3 = 0.7

The probability of having rain on each day is simply the multiplication
of having rain today and having rain tomorrow, thus
P_rain_today_and_rain_tomorrow = 0.5 * 0.4 = 0.2

(Reality might be a little bit more complex, because the chance of rain
tomorrow might dependent on the fact that it rains today)

Willem


wrote:
If the weather forcast says we have a 50% chance of rain today, and a
40% chance of rain tomorrow, what is the chance that we will have rain
during that 48 hour period? And what is the probability that we will
have rain each day during that 48 hour period?

I've tried:

P(A||B) = A + B - A * B; # Is this approach right or wrong?

P(A&&B) = (A + B) / 2;

Please, help so that I may better understand what our weather man is
really saying!


--
Willem van Deursen, The Netherlands

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