The game of pool uses 15 balls numbered from 1 to 15 (see figure). In the game of rotation, a player attempts to "sink" a ball in a pocket of the table and receives the number of points on the ba Answer the question. How many points would a player who "runs the table" receive? (To "run the table" means to sink all the balls.) points 13
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
![### Pool Game Scenario
In the game of pool, 15 balls are used, numbered from 1 to 15. Below is a detailed explanation based on the image provided.
#### Game Rules:
- The game depicted is called "rotation."
- Players aim to "sink" balls in pockets on the table.
- Players receive points equivalent to the number on the ball they sink.
#### Objective:
- The question posed is: How many points would a player score if they "run the table"? (To "run the table" means the player sinks all 15 balls.)
#### Diagram Explanation:
The diagram shows the arrangement of the 15 balls as they are positioned on the pool table:
- The balls are arranged in a triangular formation with a base of 5 balls, followed by rows of 4, 3, 2, and 1 ball at the apex.
- The balls are color-coded and numbered as follows:
- **Row 1** (Base): 4, 14, 12, 6, 15
- **Row 2**: 13, 9, 8, 3
- **Row 3**: 10, 1, 11
- **Row 4**: 2, 7
- **Row 5** (Apex): 5
The cumulative point total for sinking all balls would be the sum of the numbers 1 through 15.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F81b34105-6314-4273-8795-08495b08bba5%2Fdb1767c4-72a1-4b83-a26b-7bf13aa11645%2F0k93wv_processed.jpeg&w=3840&q=75)
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