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An experiment has four possible outcomes, labeled A to D. The probability of $A$ is $P_{A}=40 \%$ and of $B$ is $P_{B}=30 \% .$ Outcome C is twice as probable as outcome D. What are the probabilities $P_{\mathrm{C}}$ and $P_{\mathrm{D}} ?$

Name: Problem 1, Chapter 40: Physics for Scientist and Engineers: A Strategic Approach
Uploaded: 2020-07-03T18:52:30-08:00
Duration: 1 min 59 s
Channel: João Bravo
Description: An experiment has four possible outcomes, labeled A to D. The probability of A is PA=40 % and of B is PB=30 % . Outcome C is twice as probable as outcome D. What are the probabilities PC and PD ?

   An experiment has four possible outcomes, labeled A to D. The probability of $A$ is $P_{A}=40 \%$ and of $B$ is $P_{B}=30 \% .$ Outcome C is twice as probable as outcome D. What are the probabilities $P_{\mathrm{C}}$ and $P_{\mathrm{D}} ?$

Physics for Scientist and Engineers: A Strategic Approach

Randall Knight 2nd Edition

Chapter 40, Problem 1

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Solved by Expert João Bravo

07/03/2020

Step 1

So, we can write this as: \[P_{A} + P_{B} + P_{C} + P_{D} = 1\] Show more…

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An experiment has four possible outcomes, labeled A to D. The probability of $A$ is $P_{A}=40 \%$ and of $B$ is $P_{B}=30 \% .$ Outcome C is twice as probable as outcome D. What are the probabilities $P_{\mathrm{C}}$ and $P_{\mathrm{D}} ?$

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Key Concepts

Probability Distribution

This concept involves the idea that the sum of the probabilities of all possible outcomes in an experiment must equal 1, ensuring a complete and valid representation of uncertainty.

Proportional Relationships in Probability

This concept is used when the probability of one outcome is expressed as a multiple of another's. It allows for setting up a relationship between probabilities when only their ratio is provided rather than absolute values.

Solving Systems of Linear Equations

This key concept involves formulating and solving algebraic equations based on probability relationships and the total probability rule, enabling the determination of unknown probabilities from known conditions.

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