The weather is becoming important to you since you would like to go on a picnic today.If it was sunny yesterday,there is a 70% chance it will be sunny today.If it was raining yesterday,there is a 30% chance it will be sunny today.What is the probability it will be rainy today,if it was sunny yesterday?
A)0.1
B)0.2
C)0.7
D)0.8
E)0.3

Question

Quizplus · Accepted Answer

The question is asking for the probability that it will be rainy today given that it was sunny yesterday. This can be solved using Bayes' Theorem:
P(rainy today|sunny yesterday) = (P(sunny yesterday|rainy today) * P(rainy today)) / P(sunny yesterday)
We are given P(sunny yesterday) = 0.7 and P(rainy yesterday) = 0.3. We are also given that if it was sunny yesterday, there is a 70% chance it will be sunny today, which means P(sunny today|sunny yesterday) = 0.7. We need to find P(rainy today|sunny yesterday).
Using Bayes' Theorem, we can calculate:
P(rainy today|sunny yesterday) = (P(sunny yesterday|rainy today) * P(rainy today)) / P(sunny yesterday)
P(sunny yesterday|rainy today) = 0.3 (given in the question)
P(rainy today) = 0.3 (given in the question)
P(sunny yesterday) = 0.7 (given in the question)
So, we have:
P(rainy today|sunny yesterday) = (0.3 * 0.3) / 0.7 = 0.9 / 7 = 0.129 ~ 0.13
Therefore, the probability it will be rainy today, given that it was sunny yesterday, is approximately 0.13. The best choice is E.

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