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(a) The weather forecast for the weekend is a 35% chance of rain for Saturday and a 30% chance of rain for Sunday. If we assume that consecutive days are independent events, What is the probability that it rains over the weekend (either Saturday or Sunday)? Please use 3 decimal places.

(b) In fact, weather on consecutive days depends on similar atmospheric conditions and therefore consecutive days are not independent events.With the weather forecast of the previous exercise, the probability that it rains over the weekend (either Saturday or Sunday) is

Respuesta :

Answer:

Explanation:

a)

It is known that,

P(Sat) = 0.35

P(Sun) = 0.30

P(no rain on Sat) = 1 - 0.35

P(no rain on Sun) = 1 - 0.30

So P(rains on the weekend) = 1 - P(no rain on Sat) P(no rain on Sun) =

= 1 - (1-0.35)(1-0.30) = 0.545

b)

P(Sat Sun) = P(rains on Sat) P(rains on Sun) + P(rains on Sat) P(no rains on Sun)  = 0.35*0.30 + 0.35*(1-0.30) = 0.35