(a) The weather forecast for the weekend is a 46% chance of rain for Saturday an

Question

(a) The weather forecast for the weekend is a 46% chance of rain for Saturday and a 54% 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

A. 0.7516

B. 0.3758    

C. 0.2484

D. Because consecutive days are not independent, we cannot compute P(rain both days) with the information given.

Explanation / Answer

a)

weather forecast for the weekend is a 46% chance of rain for Saturday and a 54% chance of rain for Sunday

Probabilty of raining on saturday = 46% or 0.46

Probabilty of raining on sunday = 54% or 0.54

P(raining on saturday or raining on sunday) = P(raining on saturday)+P(raining on sunday)-P(raining on both saturday and sunday)

since  consecutive days are independent events

P(raining on both saturday and sunday) = P(raining on saturday)*P(raining on sunday)

= 0.46*0.54 = 0.2484

P(raining on saturday or raining on sunday) = P(raining on saturday)+P(raining on sunday)-P(raining on both saturday and sunday) = 0.46+0.54-0.2484 ~ 0.752

(b)

Given that weather on consecutive days depends on similar atmospheric conditions and therefore consecutive days are not independent events.But in the question they didn't mention how weather of one day effects the weather of other day

so Answer is (D) i.e Because consecutive days are not independent, we cannot compute P(rain both days) with the information given.

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