Probability question involving recurrence relations

In summary, a recurrence relation is a mathematical equation used to define a sequence of numbers based on previous terms. In probability, it is often used to calculate the likelihood of an event occurring over a series of trials. An example of a probability question involving a recurrence relation is the "coin flipping" problem. It differs from a recursive formula in that it is a general rule governing the entire sequence, while a recursive formula is a specific formula for calculating each term. Real-world applications of recurrence relations in probability include predicting stock prices, analyzing weather patterns, and estimating success in various trials.
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LHS
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Homework Statement



[PLAIN]http://img812.imageshack.us/img812/5261/unleduqi.png [Broken]

Homework Equations





The Attempt at a Solution




Can anyone help with part (a)ii, is pk=(1/2)^k? I can't see how to find qk
 
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1. What is a recurrence relation?

A recurrence relation is a mathematical equation that defines a sequence of numbers by expressing each term in terms of previous terms. It is often used to model real-world situations and predict future outcomes.

2. How is a recurrence relation used in probability?

In probability, recurrence relations are used to calculate the probability of an event occurring over a series of trials. They can be used to determine the likelihood of a certain outcome based on the previous outcomes.

3. Can you give an example of a probability question involving a recurrence relation?

One example of a probability question involving a recurrence relation is the classic "coin flipping" problem. If you flip a fair coin n times, what is the probability of getting exactly k heads? This can be solved using the recurrence relation P(n,k) = P(n-1,k-1) + P(n-1,k), where P(n,k) represents the probability of getting k heads in n flips.

4. What is the difference between a recurrence relation and a recursive formula?

A recurrence relation is a mathematical equation that defines a sequence, while a recursive formula is a way to generate terms in a sequence using the previous terms. In other words, a recurrence relation is a general rule that governs the entire sequence, while a recursive formula is a specific formula for calculating each term.

5. Are there any real-world applications of recurrence relations in probability?

Yes, recurrence relations have many real-world applications in probability. Some examples include predicting stock prices, analyzing weather patterns, and estimating the likelihood of success in a series of trials such as a game or sports competition.

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