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mina
20 days ago
11

In general, the probability that it rains on Saturday is 25%. If it rains on Saturday, the probability that it rains on Sunday i

s 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?
Mathematics
1 answer:
AnnZ [9K]20 days ago
5 0

Answer:

40%

Step-by-step explanation:

According to the provided information:

The likelihood of rain on Saturday stands at 25%.

P(Sunday)=25%=0.25

If it rains on Saturday, the probability of rain on Sunday rises to 50%.

P(Sunday|Saturday)=50%=0.5

If it does not rain on Saturday, the chance of Sunday rain is 25%.

P(Sunday|No Rain on Saturday)=25%=0.25

We aim to find the probability of rain 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 probabilities:

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

Thus, there is a 40% likelihood that it rained on Saturday given the conditions on Sunday.

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