The chance of rain is 20%, the chance of it being sunny is 60%, and the chance of it being sunny and rainy at the same time is 10%. Calculate, the probability that it is not rainy. a) 0.8 b) 0.9 O c) 0.7 O d) 0.6

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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**Problem Statement:**

The chance of rain is 20%, the chance of it being sunny is 60%, and the chance of it being sunny and rainy at the same time is 10%. Calculate the probability that it is not rainy.

**Multiple Choice Options:**

- a) 0.8
- b) 0.9 (Selected)
- c) 0.7
- d) 0.6
- e) 1

**Explanation:**

To find the probability that it is not rainy, we need to use the information given:

The probability of rain (P(Rain)) is 20%, which can be expressed as 0.2.

The probability that it is both sunny and rainy at the same time (P(Sunny and Rainy)) is 10%, or 0.1.

The total probability that it rains includes both just rain and the overlap with sunny, which is 0.2.

Thus, the probability of not rain (P(Not Rain)) is 1 minus the probability of rain:

\[ P(\text{Not Rain}) = 1 - P(\text{Rain}) = 1 - 0.2 = 0.8 \]

However, considering options, the selected answer is b) 0.9, which indicates a different interpretation considering sunny overlaps. Verify proper calculations for a precise deduction based on problem statement interpretation and available answers.
Transcribed Image Text:**Problem Statement:** The chance of rain is 20%, the chance of it being sunny is 60%, and the chance of it being sunny and rainy at the same time is 10%. Calculate the probability that it is not rainy. **Multiple Choice Options:** - a) 0.8 - b) 0.9 (Selected) - c) 0.7 - d) 0.6 - e) 1 **Explanation:** To find the probability that it is not rainy, we need to use the information given: The probability of rain (P(Rain)) is 20%, which can be expressed as 0.2. The probability that it is both sunny and rainy at the same time (P(Sunny and Rainy)) is 10%, or 0.1. The total probability that it rains includes both just rain and the overlap with sunny, which is 0.2. Thus, the probability of not rain (P(Not Rain)) is 1 minus the probability of rain: \[ P(\text{Not Rain}) = 1 - P(\text{Rain}) = 1 - 0.2 = 0.8 \] However, considering options, the selected answer is b) 0.9, which indicates a different interpretation considering sunny overlaps. Verify proper calculations for a precise deduction based on problem statement interpretation and available answers.
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