Chapter 4: Q.4.77 (page 169)

In the Banach matchbox problem, find the probability that at the moment when the first box is emptied (as opposed to being found empty), the other box contains exactly $k$ matches.

Short Answer

Expert verified

$P (E) = 2 \cdot (\begin{matrix} 2 N - k - 1 \\ N - 1 \end{matrix}) {(\frac{1}{2})}^{2 N - k}$

Step by step solution

Step 1:Given information

Given in the question that,we need to find find the probability that at the moment when the first box is emptied (as opposed to being found empty), the other box contains exactly $k$ matches in the Banach matchbox problem.

Step 2:Explanation

Let $E$ indicate the event that defines the moment when the first box is emptied, the other box holds exactly $k$ matches. This event will happen if and only if we make our $N$ the selecting of the right-hand box at $(2 N - k)$ the trial. Using a similar argument as in Example, we have that

$P (E) = 2 \cdot (\begin{matrix} 2 N - k - 1 \\ N - 1 \end{matrix}) {(\frac{1}{2})}^{2 N - k}$

The factor $2$ is because of the fact that the considered box is not fixed, it might be left-handed or right-handed.

Step 3:Final answer

$P (E) = 2 \cdot (\begin{matrix} 2 N - k - 1 \\ N - 1 \end{matrix}) {(\frac{1}{2})}^{2 N - k}$

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In the Banach matchbox problem, find the probability that at the moment when the first box is emptied (as opposed to being found empty), the other box contains exactly $k$ matches.

Short Answer

Step by step solution

Step 1:Given information

Step 2:Explanation

Step 3:Final answer

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In the Banach matchbox problem, find the probability that at the moment when the first box is emptied (as opposed to being found empty), the other box contains exactly kmatches.

Short Answer

Step by step solution

Step 1:Given information

Step 2:Explanation

Step 3:Final answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Probability and Statistics

Mechanics Maths

Statistics

Theoretical and Mathematical Physics

Logic and Functions

Study anywhere. Anytime. Across all devices.

In the Banach matchbox problem, find the probability that at the moment when the first box is emptied (as opposed to being found empty), the other box contains exactly $k$ matches.