Computer games in which the players take the roles of characters are very popular. They go back to earlier tabletop games such as "Dungeons & Dragons." These games use many different types of dice. A four‑sided die has faces with one of the numbers 1,2,31,2,3 , or 44 appearing at the bottom of each visible face. In this case the sample space is ?={2,3,4,5,6,7,8}S={2,3,4,5,6,7,8} . Suppose the strength of a character in a game is determined by rolling a four‑sided die twice and adding 22 to the sum of the numbers. Give a probability model (sample space and probabilities of outcomes) for the character’s strength. (a) What is the sample space of the character's strength of a character? (b) In this probability model, what is the ?(strength of a character = P(strength of a character = 4) ? (Enter your answer rounded to four decimal places.) (c) In this probability model, what is the ?(strength of a character = 9)P(strength of a character = 9) ? (Enter your answer rounded to four decimal places.)
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.
Computer games in which the players take the roles of characters are very popular. They go back to earlier tabletop games such as "Dungeons & Dragons." These games use many different types of dice. A four‑sided die has faces with one of the numbers 1,2,31,2,3 , or 44 appearing at the bottom of each visible face. In this case the
Suppose the strength of a character in a game is determined by rolling a four‑sided die twice and adding 22 to the sum of the numbers. Give a
(a) What is the sample space of the character's strength of a character?
(b) In this probability model, what is the ?(strength of a character = P(strength of a character = 4) ? (Enter your answer rounded to four decimal places.)
(c) In this probability model, what is the ?(strength of a character = 9)P(strength of a character = 9) ? (Enter your answer rounded to four decimal places.)
(d)
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