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Chapter 39: Q 1 Exercise (page 1136)

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 PCand PD?

Short Answer

Expert verified

Therefore the probabilities are:

PD=0.1PC=0.2

Step by step solution

01

Given information

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.

02

Explanation

The most crucial principle in this problem is that all conceivable outcomes' probability must add up to 1, or 100%. As a result, utilising the information provided in the problem, we can develop two equations.

PC=2PD(1)PA+PB+PC+PD=10.40+0.30+PC+PD=1PC+PD=0.3(2)

Solving (1) with (2)

role="math" localid="1648583743410" 3PD=0.3PD=0.1PC=0.2

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Most popular questions from this chapter

Physicists use laser beams to create an atom trap in which atoms are confined within a spherical region of space with a diameter of about 1mm. The scientists have been able to cool the atoms in an atom trap to a temperature of approximately 1nK, which is extremely close to absolute zero, but it would be interesting to know if this temperature is close to any limit set by quantum physics. We can explore this issue with a onedimensional model of a sodium atom in a 1.0-mm-long box.
a. Estimate the smallest range of speeds you might find for a sodium atom in this box.
b. Even if we do our best to bring a group of sodium atoms to rest, individual atoms will have speeds within the range you found in part a. Because there's a distribution of speeds, suppose we estimate that the root-mean-square speed vmsof the atoms in the trap is half the value you found in part a. Use this vrms to estimate the temperature of the atoms when they've been cooled to the limit set by the uncertainty principle.

In one experiment, 6000 photons are detected in a O.10-mm- wide strip where the amplitude of the electromagnetic wave is 200 V/m. What is the wave amplitude at a nearby 0.20-mm-wide strip where 3000 photons are detected?

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