Respuesta :
Answer:
40%
Step-by-step explanation:
From the given statements:
The probability that it rains on Saturday is 25%.
P(Sunday)=25%=0.25
Given that it rains on Saturday, the probability that it rains on Sunday is 50%.
P(Sunday|Saturday)=50%=0.5
Given that it does not rain on Saturday, the probability that it rains on Sunday is 25%.
P(Sunday|No Rain on Saturday)=25%=0.25
We are to determine the probability that it rained on Saturday given that it rained on Sunday, P(Saturday|Sunday).
P(No rain on Saturday)=1-P(Saturday)=1-0.25=0.75
Using Bayes Theorem for conditional probability:
P(Saturday|Sunday)=[TeX]\frac{P(Sunday|Saturday)P(Saturday)}{P(Sunday|Saturday)P(Saturday)+P(Sunday|No Rain on Saturday)P(No Rain on Saturday)}[/TeX]
=[TeX]\frac{0.5*0.25}{0.5*0.25+0.25*0.75}[/TeX]
=0.4
There is a 40% probability that it rained on Saturday given that it rains on Sunday.
The probability it rains on Sunday given that it rained on Saturday is;
P(A|B) = 16.67%
We are given;
Let probability that it rained on Saturday be A
Let probability that it rained on Sunday be B.
We are given;
Probability that it rains on Saturday; P(A) = 25% = 0.25
Probability that it rains on Saturday, that it rains on Sunday; P(B|A) = 50% = 0.5
Probability that if it does not rain on Saturday, then it rains on Sunday; P(B|A') = 25% = 0.25
We want to find the probability it rains on Sunday given that it rained on Saturday; P(A|B)
Using Bayes theorem for conditional probability, we have the formula;
P(A|B) = [P(B|A) × P(A)]/P(B)
We don't have P(B), Thus;
P(B) = 1 - P(B|A')
P(B) = 1 - 0.25
P(B) = 0.75
Thus;
P(A|B) = (0.5 × 0.25)/0.75
P(A|B) = 0.1667 = 16.67%
In conclusion, the probability it rains on Sunday given that it rained on Saturday is 16.67%
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