Virtually any process can be improved by use of statistics, including the law. A much publicized case that involved a debate about probability was the Collins case, which began in 1964. An incident of purse snatching in the Los Angeles area led to the arrest of Michael and Janet Collins. At their trial, an "expert" presented the probabilities listed in table below on characteristics possessed by a couple seen running from the crime scene: Characteristics Probability Man with beard 1/10 Blond woman 1/4 1/10 Yellow car Woman with ponytail Man with moustache Interracial couple 1/10 1/3 1/1000 The chance that a couple had all these characteristics together is 1 in 12 million. Because the Collises had these characteristics, the Collinses must be guilty. Do yo see any problem with this line of reasoning? Hint: The question of interest is not "what is the probability of finding a couple with these characteristics?" because one such couple has been found (the Collinses). the question is "what is the probability that another such couple exists, given that we have found one?"
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.
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