Because with replacement, the total number of possible outcomes - the denominator of the probability ratio - remains the same. Without replacement the number of possible outcomes becomes smaller.
Different lotteries have different schemes and so the probabilities are different.
Conditional probabilities arise when you revise the probabilities previously attached to some events in order to take new information into account. The revised probabilities are 'conditional on the new information you have received'.
"Without replacement" refers to a sampling method in which an item is selected from a set and then not returned to the set before the next selection. This means that each subsequent selection is made from a reduced pool of items, affecting the probabilities of choosing each item. This concept is commonly used in statistics and probability theory, particularly in scenarios involving drawing cards from a deck or selecting objects from a collection.
Selecting a card and then selecting again without replacement is a dependent event. This is because the outcome of the second selection is influenced by the result of the first selection; the total number of cards decreases and potentially alters the probabilities of the remaining cards. Thus, the events are not independent, as the probability of selecting a specific card in the second draw depends on what was drawn in the first.
I do not add probabilities to anybody!
Different lotteries have different schemes and so the probabilities are different.
Conditional probabilities arise when you revise the probabilities previously attached to some events in order to take new information into account. The revised probabilities are 'conditional on the new information you have received'.
Assumptions are statements or beliefs taken for granted without proof, often serving as a foundation for reasoning or decision-making. Probabilities, on the other hand, are quantitative measures that express the likelihood of an event occurring, usually represented as a number between 0 and 1. While assumptions can be subjective and vary between individuals, probabilities are typically derived from data and statistical analysis. Thus, assumptions can influence how probabilities are interpreted, but they are fundamentally different concepts.
Selecting a card and then selecting again without replacement is a dependent event. This is because the outcome of the second selection is influenced by the result of the first selection; the total number of cards decreases and potentially alters the probabilities of the remaining cards. Thus, the events are not independent, as the probability of selecting a specific card in the second draw depends on what was drawn in the first.
"Without replacement" refers to a sampling method in which an item is selected from a set and then not returned to the set before the next selection. This means that each subsequent selection is made from a reduced pool of items, affecting the probabilities of choosing each item. This concept is commonly used in statistics and probability theory, particularly in scenarios involving drawing cards from a deck or selecting objects from a collection.
The conservative approach
I do not add probabilities to anybody!
Empirical probabilities.
Yes, but that might not always make sense.
It refers to experiments where more than one tokens are randomly selected from a set of tokens (of different colours). If the the token is replaced after each selection, the probabilities remain constant whereas if the token is not replaced - as the question suggests - the probabilities change, depending on the outcome of the selection.It refers to experiments where more than one tokens are randomly selected from a set of tokens (of different colours). If the the token is replaced after each selection, the probabilities remain constant whereas if the token is not replaced - as the question suggests - the probabilities change, depending on the outcome of the selection.It refers to experiments where more than one tokens are randomly selected from a set of tokens (of different colours). If the the token is replaced after each selection, the probabilities remain constant whereas if the token is not replaced - as the question suggests - the probabilities change, depending on the outcome of the selection.It refers to experiments where more than one tokens are randomly selected from a set of tokens (of different colours). If the the token is replaced after each selection, the probabilities remain constant whereas if the token is not replaced - as the question suggests - the probabilities change, depending on the outcome of the selection.
Sum of all probabilities is 1.
as you cannot get more than 1