The weather forecaster says that the probability of rain on Saturday i

Sherry Becker

Sherry Becker

Answered question

2021-11-16

The weather forecaster says that the probability of rain on Saturday is 20% and the probability of rain on Sunday is 30%
a. Can you estimate the likelihood that it will rain this weekend (Saturday or Sunday)?

Answer & Explanation

Unpled

Unpled

Beginner2021-11-17Added 23 answers

Step 1 
Given: According to the weather forecaster, Saturday's chances of rain are is 20% and the probability of rain on Sunday is 30%
Probability of rain on Saturday: 20%=0.2 
Probability of rain on Sunday: 30%=0.3 
Probability of rain over the weekend=Probability of rain on at least one of the days over the weekend (Saturday or Sunday or Both days) 
Therefore, the Probability of rain over the weekend=1Probability of no rain over the weekend 
Step 2 
Probability of no rain on Saturday: 10.2=0.8 
Probability of no rain on Sunday: 10.3=0.7 
Thus, the likelihood that neither of the days will see any precipitation (probability of no precipitation over the weekend): (0.8)(0.7)=0.56 
Probability of rain over the weekend=1Probability of no rain over the weekend. 
Probability of rain over the weekend: 10.56=0.44 Thus, the probability of rain over the weekend is 0.44.

Don Sumner

Don Sumner

Skilled2023-05-27Added 184 answers

Result:
44% or 0.44
Solution:
Let's denote the event of rain on Saturday as A and the event of rain on Sunday as B. The probability of rain on Saturday is given as 20%, which can be written as P(A)=0.20. Similarly, the probability of rain on Sunday is given as 30%, which can be written as P(B)=0.30.
To estimate the likelihood of rain this weekend (either Saturday or Sunday), we can use the concept of union of events. The union of events A and B (denoted as AB) represents the event of rain on either Saturday or Sunday or both.
The probability of the union of two events can be calculated using the formula:
P(AB)=P(A)+P(B)P(AB)
Here, P(AB) represents the probability of both events A and B occurring simultaneously.
However, we don't have information about the probability of rain occurring on both Saturday and Sunday. So, to estimate the likelihood of rain this weekend, we can assume that the events A and B are independent. This assumption implies that the occurrence of rain on one day does not affect the occurrence of rain on the other day.
If the events A and B are independent, then the probability of their intersection is given by:
P(AB)=P(A)·P(B)
Substituting this into the formula for the union of events, we get:
P(AB)=P(A)+P(B)P(A)·P(B)
Now, let's substitute the given probabilities into this formula:
P(AB)=0.20+0.300.20·0.30
Simplifying the expression:
P(AB)=0.20+0.300.06=0.44
Therefore, the estimated likelihood that it will rain this weekend (either Saturday or Sunday) is 44% or 0.44.
nick1337

nick1337

Expert2023-05-27Added 777 answers

To find the likelihood that it will rain this weekend (either on Saturday or Sunday), we need to calculate the probability of rain on Saturday (P(S)) or rain on Sunday (P(S)). This can be done using the formula:
P(S or S)=P(S)+P(S)P(S and S)
Since the events 'rain on Saturday' and 'rain on Sunday' are mutually exclusive (if it rains on one day, it cannot rain on the other), we can assume that P(S and S)=0.
Substituting the given probabilities into the formula, we get:
P(S or S)=0.20+0.300=0.50
Therefore, the estimated likelihood of rain this weekend is 50%.
RizerMix

RizerMix

Expert2023-05-27Added 656 answers

To estimate the likelihood of rain this weekend (Saturday or Sunday), we can use the concept of probability and apply the principle of addition.
Let's denote the event of rain on Saturday as A and the event of rain on Sunday as B. The given probabilities are P(A)=0.20 (20% chance of rain on Saturday) and P(B)=0.30 (30% chance of rain on Sunday).
The likelihood of rain this weekend can be estimated by calculating the probability of either rain on Saturday or rain on Sunday. We denote this event as AB, which represents the union of events A and B.
The probability of the union of two events can be calculated using the formula:
P(AB)=P(A)+P(B)P(AB)
where P(AB) represents the probability of both events A and B occurring simultaneously.
Since we don't have any information about the intersection of events A and B in this scenario, we assume they are independent. Therefore, we can assume P(AB)=P(A)·P(B).
Plugging in the given probabilities:
P(AB)=P(A)+P(B)P(A)·P(B)
Substituting the values:
P(AB)=0.20+0.30(0.20·0.30)
Simplifying the expression:
P(AB)=0.500.06
P(AB)=0.44
Therefore, the estimated likelihood that it will rain this weekend (Saturday or Sunday) is 44%, or 0.44 in decimal form.

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