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Find out about the company’s plan: they want to earn $500k profit in 2 years, but it’s only likely to happen 30% of the time. See what they think they’ll make on average!
The company wants to hit 1/2 a million $s in profit in 2 years. The CEO believes the probability of achieving this is 0.30. What is the expected value?
The expected value is $150,000.
To calculate the expected value (EV), you multiply the value of each possible outcome by its probability of occurring and then sum up these values.
In this scenario:
- If the company hits $500,000 profit, the value is $500,000.
- If the company does not hit $500,000 profit, the value is $0.
Given that the CEO believes the probability of achieving this target is 0.30 and the probability of not achieving it is (1 – 0.30) = 0.70:
EV = (Probability of hitting target * Value if target hit) + (Probability of not hitting target * Value if target not hit)
EV = (0.30 * $500,000) + (0.70 * $0) EV = $150,000 + $0 EV = $150,000
So, the expected value is $150,000.
What is Probability Theory?
Probability theory is a branch of mathematics that deals with the study of random phenomena or uncertain events. It provides a framework for quantifying uncertainty and reasoning about the likelihood of various outcomes occurring. In probability theory, events are typically assigned probabilities, which represent the likelihood of their occurrence. These probabilities obey certain mathematical rules and can be manipulated to analyze complex situations involving randomness.
Key concepts in probability theory include:
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Random variables: These are variables that can take on different values as a result of random processes. Each value has an associated probability.
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Probability distributions: These describe the probabilities of different outcomes for a random variable. Common probability distributions include the uniform distribution, normal distribution, binomial distribution, and Poisson distribution, among others.
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Events and outcomes: An event is a set of outcomes of a random experiment. The probability of an event is the sum of the probabilities of the outcomes in that event.
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Conditional probability: This is the probability of an event occurring given that another event has already occurred. It is denoted by P(A|B), the probability of event A given that event B has occurred.
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Independence: Two events are independent if the occurrence of one event does not affect the probability of the other event occurring.
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Bayes’ theorem: This theorem describes how to update the probability of an event based on new evidence or information.
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Expectation and variance: These are measures of central tendency and variability, respectively, for a random variable.
Probability theory has numerous applications across various fields, including statistics, finance, engineering, physics, biology, and computer science. It is used to model and analyze uncertainty in systems, make predictions, and guide decision-making under uncertainty.
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Source: Math Hello Kitty
Categories: Math
