Tough (algebraic) probability problem.

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In summary, there are an infinite number of ordered pairs (b,y) of positive integers with 4 \le b \le y \le 2007 that satisfy the given condition. This can be proven using a simple formula for calculating the probability of the balls on each end having the same color. Additionally, there is currently no button that automatically adds LaTeX tags, but it may be useful to look into using a text editor or browser extension that supports LaTeX formatting.
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mathwizarddud
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How many ordered pairs [tex](b,y)[/tex] of positive integers with [tex]4 \le b \le y \le 2007[/tex] are there such that when [tex]b[/tex] blue balls and [tex]y[/tex] yellow balls are randomnly arranged in a row, the probability that the balls on each end have the same colour is [tex]1/2[/tex]?

PS: Is there a button such that I could just click on it after I highlighted the text that I want to be included in the LaTeX tags? It's going to save me a lot of typing if there's such button (without keep typing [tex] and so on)!
 
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This just looks like some conditional probability problem. Is it homework, a challenge for the rest of us, or something else?
 

What is a "tough (algebraic) probability problem"?

A tough (algebraic) probability problem is a math problem that involves using algebraic equations and concepts to solve a probability question. These types of problems often require a deep understanding of algebra, as well as knowledge of probability theory, to successfully solve.

Why are "tough (algebraic) probability problems" challenging?

Tough (algebraic) probability problems are challenging because they require a combination of skills in both algebra and probability. They often involve complex equations and multiple steps to arrive at a solution. Additionally, these problems may require creative thinking and the ability to identify and apply the correct algebraic concepts to solve the given probability question.

How can I approach solving a "tough (algebraic) probability problem"?

One approach to solving a tough (algebraic) probability problem is to break it down into smaller, more manageable parts. Start by identifying what information is given and what is being asked in the problem. Then, use your knowledge of algebra and probability to create equations and solve for the unknown variables. It may also be helpful to draw diagrams or make a table to organize the information and make the problem easier to understand.

What are some common strategies for solving "tough (algebraic) probability problems"?

Some common strategies for solving tough (algebraic) probability problems include using basic probability rules, such as the addition and multiplication rules, and setting up equations based on the given information. It may also be helpful to use visual aids, such as diagrams or tables, to better understand the problem and identify patterns. Additionally, trying different approaches and using trial and error can also be effective strategies for solving these types of problems.

Where can I find practice "tough (algebraic) probability problems" to improve my skills?

There are many resources available online and in textbooks that provide practice tough (algebraic) probability problems. Some websites, such as Khan Academy and MathisFun, offer free tutorials and practice problems to help improve your skills. You can also find practice problems in algebra and probability textbooks or by searching for specific topics or concepts on search engines.

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