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Ch 39: Wave Functions and Uncertainty
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoKnight Calc 5th EditionCh 39: Wave Functions and UncertaintyProblema 1
Capitolo 39, Problema 1

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?

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Step 1: Start by understanding the problem. You are given probabilities for outcomes A and B, and a relationship between outcomes C and D. The total probability for all outcomes must sum to 100% (or 1 in decimal form).
Step 2: Write the equation for the total probability: Pₐ + PB + PC + PD = 1. Substitute the given values for Pₐ and PB: 0.40 + 0.30 + PC + PD = 1.
Step 3: Use the relationship between outcomes C and D. The problem states that outcome C is twice as probable as outcome D, so PC = 2 × PD.
Step 4: Substitute PC = 2 × PD into the total probability equation: 0.40 + 0.30 + 2 × PD + PD = 1.
Step 5: Combine like terms and solve for PD. Once PD is found, use the relationship PC = 2 × PD to calculate PC.

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Probability Basics

Probability is a measure of the likelihood that an event will occur, expressed as a number between 0 and 1, or as a percentage. The sum of the probabilities of all possible outcomes in a given experiment must equal 1 (or 100%). Understanding this principle is crucial for solving problems involving multiple outcomes.
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Probability Distribution Graph

Setting Up Equations

In problems involving probabilities, it is often necessary to set up equations based on the relationships between different outcomes. For instance, if one outcome is defined in terms of another (like C being twice as probable as D), this relationship can be expressed mathematically to find unknown probabilities.
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Solving for Unknowns

Once the equations are established, solving for unknown probabilities involves algebraic manipulation. This may include substituting known values and simplifying equations to isolate the variable of interest. Mastery of these techniques is essential for determining the probabilities of outcomes in complex scenarios.
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Pratica correlata
Domanda del libro di testo

When 5×1012 photons pass through an experimental apparatus, 2.0×109 land in a 0.10-mm-wide strip. What is the probability density at this point?

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Domanda del libro di testo

In one experiment, 2000 photons are detected in a 0.10-mm-wide strip where the amplitude of the electromagnetic wave is 10 V/m. How many photons are detected in a nearby 0.10-mm-wide strip where the amplitude is 30 V/m?

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Domanda del libro di testo

FIGURE EX39.12 shows the probability density for an electron that has passed through an experimental apparatus. If 1.0×106 electrons are used, what is the expected number that will land in a 0.010-mm-wide strip at 2.000 mm?

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