Conditional Probability and Independence
... Two events A and B are independent if the occurrence of one event has no effect on the chance that the other event will happen. In other words, events A and B are independent if P(A | B) = P(A) and P(B | A) = P(B). Example Lefties Down Under (Checking for independence) Is there a relationship betwee ...
... Two events A and B are independent if the occurrence of one event has no effect on the chance that the other event will happen. In other words, events A and B are independent if P(A | B) = P(A) and P(B | A) = P(B). Example Lefties Down Under (Checking for independence) Is there a relationship betwee ...
probability-stats
... without distinction. I was in the top 98% of my class and damn glad to be there. I slept in the library and daydreamed my way through history lecture. I failed math twice, never fully grasping probability theory. I mean, first off, who cares if you pick a black ball or a white ball out of the bag? A ...
... without distinction. I was in the top 98% of my class and damn glad to be there. I slept in the library and daydreamed my way through history lecture. I failed math twice, never fully grasping probability theory. I mean, first off, who cares if you pick a black ball or a white ball out of the bag? A ...
Student sheets Word
... For example, on the dice P(7) = 0. The probability of something that is certain is 1. For example, on the dice P(score < 7) = 1. These results can all be shown on a probability line: ...
... For example, on the dice P(7) = 0. The probability of something that is certain is 1. For example, on the dice P(score < 7) = 1. These results can all be shown on a probability line: ...
Algebra 1 - Comments on
... Another way to describe the chance of an event occurring is with odds. The odds in favor of an event is the ratio that compares the number of ways the event can occur to the number of ways the event cannot occur. ...
... Another way to describe the chance of an event occurring is with odds. The odds in favor of an event is the ratio that compares the number of ways the event can occur to the number of ways the event cannot occur. ...
Theoretical Probability
... There is no standard notation for permutations; this is because it can be done with the standard notation for combinations and factorials. The middle (or second) item in the formula is probably most common (though there are others). For example, let's say that I've decided to complete my domination ...
... There is no standard notation for permutations; this is because it can be done with the standard notation for combinations and factorials. The middle (or second) item in the formula is probably most common (though there are others). For example, let's say that I've decided to complete my domination ...
2. Define B1, B2, B3 to be the events Box 1, 2 or 3, is selected
... • Box 1 has two gold coins • Box 2 has one gold coin and one silver. • Box 3 has two silver coins. • Suppose that you select one of the boxes randomly and then select one of the coins from this box. Question: What is the probability that the coin you select a gold coin? Solution: 1. Let’s event A is ...
... • Box 1 has two gold coins • Box 2 has one gold coin and one silver. • Box 3 has two silver coins. • Suppose that you select one of the boxes randomly and then select one of the coins from this box. Question: What is the probability that the coin you select a gold coin? Solution: 1. Let’s event A is ...
Section 6.2: Definition of Probability
... determined by random selection. Suppose that this week a member of the offensive team will call the toss. There are 5 interior linemen on the 11-player offensive team. If we define the event L as the event that lineman is selected to call the toss, 5 of the 11 possible outcomes are included in L. Th ...
... determined by random selection. Suppose that this week a member of the offensive team will call the toss. There are 5 interior linemen on the 11-player offensive team. If we define the event L as the event that lineman is selected to call the toss, 5 of the 11 possible outcomes are included in L. Th ...
Probability --
... So, e.g., k = 20, then there exists a Red/Blue coloring of the complete graph with 2^10 – 1 = 1023 nodes that does not have any complete monochromatic sub graph of size 20. (But we have no idea of how to find such a coloring!) Proof: Consider a sample space where each possible coloring of the n-node ...
... So, e.g., k = 20, then there exists a Red/Blue coloring of the complete graph with 2^10 – 1 = 1023 nodes that does not have any complete monochromatic sub graph of size 20. (But we have no idea of how to find such a coloring!) Proof: Consider a sample space where each possible coloring of the n-node ...
Ars Conjectandi
Ars Conjectandi (Latin for The Art of Conjecturing) is a book on combinatorics and mathematical probability written by Jakob Bernoulli and published in 1713, eight years after his death, by his nephew, Niklaus Bernoulli. The seminal work consolidated, apart from many combinatorial topics, many central ideas in probability theory, such as the very first version of the law of large numbers: indeed, it is widely regarded as the founding work of that subject. It also addressed problems that today are classified in the twelvefold way, and added to the subjects; consequently, it has been dubbed an important historical landmark in not only probability but all combinatorics by a plethora of mathematical historians. The importance of this early work had a large impact on both contemporary and later mathematicians; for example, Abraham de Moivre.Bernoulli wrote the text between 1684 and 1689, including the work of mathematicians such as Christiaan Huygens, Gerolamo Cardano, Pierre de Fermat, and Blaise Pascal. He incorporated fundamental combinatorial topics such as his theory of permutations and combinations—the aforementioned problems from the twelvefold way—as well as those more distantly connected to the burgeoning subject: the derivation and properties of the eponymous Bernoulli numbers, for instance. Core topics from probability, such as expected value, were also a significant portion of this important work.