Questions: If it rains today, the probability of rain tomorrow is higher due to the current weather pattern. The probability of rain on any given day is 30%, but if it rains today, the probability of rain tomorrow is 50%. What is the probability that it will rain today and tomorrow? Input your answer as a decimal. Round your answer to two decimal places.

If it rains today, the probability of rain tomorrow is higher due to the current weather pattern. The probability of rain on any given day is 30%, but if it rains today, the probability of rain tomorrow is 50%. What is the probability that it will rain today and tomorrow? Input your answer as a decimal. Round your answer to two decimal places.
Transcript text: Section 3.3 Homework - MATH-1410-0-Elementary Probability and Statistics I-(82903)-Fall 2024 /le/content/17161/viewContent/783711/Niew Homework Previous Page Next Page Page 8 of 10 Question 8 (1 point) Listen If it rains today, the probability of rain tomorrow is higher due to the current weather pattern. The probability of rain on any given day is 30\%, but if it rains today, the probability of rain tomorrow is $50 \%$. What is the probability that it will rain today and tomorrow? Input your answer as a decimal. Round your answer to two decimal places. Page 8 of 10 Previous Page Next Page Submit Quiz 0 of 10 questions saved
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Solution

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Solution Steps

Step 1: Identify Given Probabilities
  • Probability of rain on any given day (P(Rain)) = 0.30
  • Probability of rain tomorrow if it rains today (P(Rain Tomorrow | Rain Today)) = 0.50
Step 2: Calculate Joint Probability
  • We need to find the probability that it will rain today and tomorrow.
  • This is the product of the probability of rain today and the conditional probability of rain tomorrow given that it rains today.
Step 3: Apply the Multiplication Rule
  • P(Rain Today and Rain Tomorrow) = P(Rain Today) * P(Rain Tomorrow | Rain Today)
  • P(Rain Today and Rain Tomorrow) = 0.30 * 0.50 = 0.15

Final Answer

The probability that it will rain today and tomorrow is 0.15.

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