Question

Weather Prediction There is a $50 \%$ chance of rain today and a $50 \%$ chance of rain tomorrow. Assuming that the event that it rains today is independent of the event that it rains tomorrow, draw a tree diagram showing the probabilities of all outcomes. What is the probability that there will be no rain today or tomorrow?

Name: Problem 67, Chapter 7: Finite Mathematics and Applied Calculus
Uploaded: 2021-12-07T18:34:57-08:00
Duration: 2 min 2 s
Channel: Lucas Finney
Description: Weather Prediction There is a 50 % chance of rain today and a 50 % chance of rain tomorrow. Assuming that the event that it rains today is independent of the event that it rains tomorrow, draw a tree diagram showing the probabilities of all outcomes. What is the probability that there will be no rain today or tomorrow?

   Weather Prediction There is a $50 \%$ chance of rain today and a $50 \%$ chance of rain tomorrow. Assuming that the event that it rains today is independent of the event that it rains tomorrow, draw a tree diagram showing the probabilities of all outcomes. What is the probability that there will be no rain today or tomorrow?

Finite Mathematics and Applied Calculus

Stefan Waner, Steven… 5th Edition

Chapter 7, Problem 67

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Solved by Expert Lucas Finney

12/07/2021

Step 1

We have two events: it rains today (D1) and it rains tomorrow (D2). Each event has two possible outcomes: it rains (R) or it doesn't rain (R'). The probability of each outcome is 50%, or 0.5. The tree diagram would look like this: ``` D1 / \ R1 R1' 0.5 0.5 | Show more…

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Weather Prediction There is a $50 \%$ chance of rain today and a $50 \%$ chance of rain tomorrow. Assuming that the event that it rains today is independent of the event that it rains tomorrow, draw a tree diagram showing the probabilities of all outcomes. What is the probability that there will be no rain today or tomorrow?

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Key Concepts

Independent Events

Independent events are events where the outcome of one does not affect the outcome of the other. This concept is crucial in probability calculations because it allows the probability of combined events to be determined by multiplying their individual probabilities.

Tree Diagrams

A tree diagram is a visual tool used to map out all possible outcomes of a probabilistic scenario. It helps in organizing the sequence of events and their corresponding probabilities, making it easier to handle compound events and calculate overall probabilities.

Multiplication Rule

The Multiplication Rule states that for two independent events, the probability of both events occurring is the product of their individual probabilities. This rule simplifies the process of finding the probability of joint occurrences in independent scenarios.

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