Show that the probability of scroing exactly n points is

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
  • #1
nowimpsbball
15
0

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


Homework Equations





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

Related to Show that the probability of scroing exactly n points is

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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