Poker is a common game in which players are dealt five cards from a deck of cards. It can be shown that there are 2,598,960 different possible poker hands. The winning hands (from highest to lowest) are shown in the table below. Find the requested probability. Use a calculator. (Show your answer to nine decimal places.) P(four of a kind) Poker Hands Royal flush 4 hands Other straight flush 36 hands Four of a kind 624 hands Full house 3,744 hands Flush 5,108 hands Straight 10,200 hands Three of a kind 54,912 hands Two pair 123,552 hands One pair 1,098,240 hands Other hands 1,302,540 hands
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
Tree diagram
Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
*All of these probabilities are mutually exclusive. That is, the 36 straight flushes do not include the 4 royal flushes, and the 5,108 flush hands do not include the better hands of straight flush or royal flush.
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
