Question

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?

Answer 1

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)=$\frac{P(Sunday|Saturday)P(Saturday)}{P(Sunday|Saturday)P(Saturday)+P(Sunday|No Rain on Saturday)P(No Rain on Saturday)}$

=$\frac{0.5*0.25}{0.5*0.25+0.25*0.75}$

=0.4

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