1.22 The U.S. National Weather Service issues Probability of Precipitation (PoP)

Question

1.22 The U.S. National Weather Service issues Probability of Precipitation (PoP) reports. A report might indicate a 30% chance of rain. a. What does this mean? b. What is the PoP definition of the following terms: slight chance, chance, likely? A comic strip made the following statements: 1.23 . "There's a 60% chance of rain on Saturday" (denoted Si). . "There's a 40% chance of rain on Sunday" (denoted S2). . "Therefore, there's a 100% chance of rain this weekend" (denoted S3). a. Given that S1 and S2 true, can the third statement, S3, be true? Why or why not? b. Given SI and S2 are true, what is the smallest possible probability of rain this weekend, and what is the largest possible probability of rain this weekend? c. Explain how the lower and upper bounds in part b can be achieved d. If S1 and S2 are independent, what is the probability of rain this weekend?

Explanation / Answer

1.22 a) it means only 30% of the forecast area get the rain. this may be obtained based on the past performances in the previous season during the same time or based on the weather report in the past few days..Inother words this means there are chances of rain in few places of the geograhic area (30%) and rest has no rain.if an area is randomly selected chances that it gets rain is 30%

b)Mathematically, PoP is defined as follows:

PoP = C x A where "C" = the confidence that precipitation will occur in the forecast area, and where "A" = the percent of the area that will receive precipitation

Slight chance means very few places in the forecast area receives the rain.. likely is the likelyhood of rain in the forecst area.

1.23) a) not true...60% is the confidence level of getting rain on saturday... so chances of no rain on saturday is 40%

Statistically if we try to find the probability of rain this week end.

Ie probability of rain on saturday or sunday= probabilty of rain on sunday+ probability of rain on saturday-probability of rain on sunday and saturday.

. since the events are not mutually exclusive . (Mutually exclusive means happening of one event doesnt include the other) there is a non zero chance for the last probability which we are not aware of

b) smallest possible probability of rain this week end is 40% = 0.4

Largest probability =60%=0.6

c)we have only two possibility of rain 40% and 60%.... the smallest of these will be the lower bound... as this probability indicates 40% of the forecast area gets rain. And the latgest of these two is 60%... which assures 60% of forcast area getting the rain

D) if both are independent then

P(S1 & S2) = P(S1)* P(S2) =40% * 60% =24%

Probability of rain this week end can be calculated using the addition theorem

P(S1 or S2) = P(S1) + P(S2)-P(S1 & S2) = 0.6+0.4-0.24=0.76

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