# Show that the probability of scroing exactly n points is

• nowimpsbball
In summary, the formula for calculating the probability of scoring exactly n points is P(n) = (total number of ways to score n points) / (total number of possible outcomes). To determine the total number of ways to score n points, the scoring system can be broken down into individual events and the combinations of these events can be calculated. The difference between the probability of scoring exactly n points and the probability of scoring at least n points is that the former only includes the specific number of points, while the latter includes that number and all higher point totals. The probability of scoring exactly n points cannot be greater than 1 as it is a measure of likelihood. This concept can be applied in real life situations such as predicting game outcomes or analyzing
nowimpsbball

## Homework Statement

A player tosses a coin repeatedly. Heads is one point, tails is two points. A player tosses until his score equals or exceeds n. Show that the probability of scoring exactly n points is (2+(-1/2)^n)/3

## The Attempt at a Solution

My guess would be a proof by induction, but not really sure how to go about this or any attempted proof

Thanks

Seems pretty straightforward to me. Why don't you start by doing the initial cases (n=1,2) and writing out the inductive step?

## 1. What is the formula for calculating the probability of scoring exactly n points?

The formula for calculating the probability of scoring exactly n points is P(n) = (total number of ways to score n points) / (total number of possible outcomes).

## 2. How do you determine the total number of ways to score n points?

The total number of ways to score n points can be determined by breaking down the scoring system into individual events and calculating the combinations of these events that result in a total of n points.

## 3. What is the difference between the probability of scoring exactly n points and the probability of scoring at least n points?

The probability of scoring exactly n points refers to the likelihood of scoring exactly that number of points, while the probability of scoring at least n points includes that number and all higher point totals.

## 4. Can the probability of scoring exactly n points be greater than 1?

No, the probability of scoring exactly n points cannot be greater than 1 as it is a measure of likelihood and must fall between 0 and 1.

## 5. How can the probability of scoring exactly n points be applied in real life situations?

The probability of scoring exactly n points can be used in various scenarios, such as predicting the outcome of a game or determining the chances of winning a contest with a specific point system. It can also be used in statistics and data analysis to understand patterns and trends in scoring.

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