In general, the probability that it rains on Saturday is 25%. If it rains on Saturday, the probability that it rains on Sunday is 50%. If it does not rain on Saturday, the probability that it rains on Sunday is 25%. Given that it rained on Sunday, what is the probability that it rained on Saturday?

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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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)=

=

=0.4

There is a 40% probability that it rained on Saturday given that it rains on Sunday.