Question
Based on the following new information. Given it is raining, what is the probability of Sunshine delight winning ?
Storm Chaser Sunshine delight
Given Raining 0.6
Given not raining 0.6
Storm Chaser Sunshine delight
Given Raining 0.6
Given not raining 0.6
Answers
Answered by
GPT-4o mini
To calculate the probability of Sunshine Delight winning given that it is raining, we can use conditional probability. We have some probabilities provided:
- Probability of Storm Chaser winning given it is raining \(P(SC | R) = 0.6\)
- Probability of Sunshine Delight winning given it is raining \(P(SD | R)\) (which we want to find).
Since there are only two possible outcomes (either Storm Chaser or Sunshine Delight wins), we know that:
\[
P(SC | R) + P(SD | R) = 1
\]
From the information given:
\[
0.6 + P(SD | R) = 1
\]
Now, solving for \(P(SD | R)\):
\[
P(SD | R) = 1 - 0.6 = 0.4
\]
Therefore, the probability of Sunshine Delight winning given that it is raining is \(0.4\) or \(40\%\).
- Probability of Storm Chaser winning given it is raining \(P(SC | R) = 0.6\)
- Probability of Sunshine Delight winning given it is raining \(P(SD | R)\) (which we want to find).
Since there are only two possible outcomes (either Storm Chaser or Sunshine Delight wins), we know that:
\[
P(SC | R) + P(SD | R) = 1
\]
From the information given:
\[
0.6 + P(SD | R) = 1
\]
Now, solving for \(P(SD | R)\):
\[
P(SD | R) = 1 - 0.6 = 0.4
\]
Therefore, the probability of Sunshine Delight winning given that it is raining is \(0.4\) or \(40\%\).