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)0.3
D)0.4

Question

Quizplus · Accepted Answer

The problem only gives the probability of it being sunny given the weather from the day before. It does not give any information about the probability of it being rainy given the weather from the day before. Therefore, we cannot determine the answer with certainty. However, we can use Bayes' theorem to make an educated guess.

Let R be the event that it is rainy today and S be the event that it was sunny yesterday. We want to find P(R|S), the probability that it will be rainy today given that it was sunny yesterday.

Using Bayes' theorem, we have:

P(R|S) = P(S|R) * P(R) / P(S)

We know that P(S|R) = 0.3 (the probability that it will be sunny today given that it was raining yesterday is 0.3). We also know that P(R) is not given, but it is reasonable to assume that it is less than 0.5 (since the problem implies that there is a higher chance of it being sunny than rainy). Finally, we know that:

P(S) = P(S|R) * P(R) + P(S|not R) * P(not R)
     = 0.3 * P(R) + 0.7 * P(not R)

We can guess that P(not R) is close to 1 (since it was sunny yesterday) and therefore P(R) is close to 0. So, we have:

P(S) ≈ 0.3 * 0 + 0.7 * 1
    ≈ 0.7

Putting it all together, we have:

P(R|S) ≈ 0.3 * 0 / 0.7
      ≈ 0

This means that it is very unlikely to be rainy today given that it was sunny yesterday. Out of the answer choices, the closest one to 0 is 0.3 (C).

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