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princejan7
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Homework Statement
My book says that
P(C∩G) = P(G)P(C|G)
but shouldn't it be
P(C∩G)= P(C)P(C|G)
?
No. To see why, consider the case where ##C## and ##G## are independent. Then we expect ##P(C|G) = P(C)## and ##P(C \cap G) = P(C)P(G)##. That is consistent with the formula from the book, not your proposed formula.princejan7 said:Homework Statement
My book says that
P(C∩G) = P(G)P(C|G)
but shouldn't it be
P(C∩G)= P(C)P(C|G)
princejan7 said:Homework Statement
My book says that
P(C∩G) = P(G)P(C|G)
but shouldn't it be
P(C∩G)= P(C)P(C|G)
?
Homework Equations
The Attempt at a Solution
Perhaps you are misreading the notation. P(C|G) means the probability of the event C given that event G occurs. Maybe you read it as the other way around?princejan7 said:My book says that
P(C∩G) = P(G)P(C|G)
but shouldn't it be
P(C∩G)= P(C)P(C|G)
Simple probability is a branch of mathematics that deals with the likelihood or chance of an event occurring. It is a way to quantify uncertainty and make predictions based on data and assumptions.
Simple probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. This can be represented by the formula P(A) = number of favorable outcomes / total number of possible outcomes.
Simple probability deals with a single event, while compound probability deals with multiple events occurring together. In simple probability, each event is independent and does not affect the outcome of other events. In compound probability, the events may be dependent on each other.
The sample space is the set of all possible outcomes in a given situation. It is important in simple probability as it helps to determine the total number of possible outcomes and calculate the probability of a specific event occurring.
Simple probability is used in many real-life situations, such as predicting the weather, calculating the chances of winning a game, or estimating the likelihood of a certain event happening. It is also used in risk assessment and decision making in fields such as finance, insurance, and healthcare.