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Apr 15, 2024 · Essentially, conditional probability is the likelihood of an event occurring, assuming a different one has already happened. Otherwise said, there must be some sort of relationship with the past. Moreover, its formula, which we will expand on in this tutorial, is based on the Bayes’ Theorem .
The conditional probability formula gives the measure of the probability of an event, say B given that another event, say A has occurred. The Bayes' theorem is used to determine the conditional probability of event A, given that event B has occurred, by knowing the conditional probability of event B, given that event A has occurred, also the individual probabilities of events A and B.
Aug 17, 2020 · In addition to its properties as a probability measure, conditional probability has special properties which are consequences of the way it is related to the original probability measure \(P(\cdot)\). The following are easily derived from the definition of conditional probability and basic properties of the prior probability measure, and prove useful in a variety of problem situations.
Conditional Probability. The conditional probability of an event A given that an event B has occurred is written: P ( A | B) and is calculated using: P ( A | B) = P ( A ∩ B) P ( B) as long as P ( B) > 0.
Example \(\PageIndex{1}\) For an example of conditional distributions for discrete random variables, we return to the context of Example 5.1.1, where the underlying probability experiment was to flip a fair coin three times, and the random variable \(X\) denoted the number of heads obtained and the random variable \(Y\) denoted the winnings when betting on the placement of the first heads obtained in the three flips.
For example, 3 of these 36 equally likely outcomes correspond to rolling a sum of 10, so the probability of rolling a 10 is 3 36 = 1 12 3 36 = 1 12.However, if you choose to roll the dice one at a time, the probability of rolling a 10 will change after the first die comes to rest.
Feb 6, 2021 · Let's calculate the conditional probability of \(A\) given \(D\), i.e., the probability that at least one heads is recorded (event \(A\)) assuming that at least one tails is recorded (event \(D\)). Recalling that outcomes in this sample space are equally likely, we apply the definition of conditional probability (Definition 2.2.1) and find
