When playing roulette at a​ casino, a gambler is trying to decide whether to bet ​$15 on the number 13 or to bet ​$15 that the outcome is any one of the three possibilities 00, 0, or 1. The gambler knows that the expected value of the ​$15 bet for a single number is −0.79¢. For the ​$15 bet that the outcome is 00, 0, or 1​, there is a probability of 338 of making a net profit of ​$60 and a 3538 probability of losing ​$15. a. Find the expected value for the ​$15 bet that the outcome is 00, 0, or 1. b. Which bet is​ better: a ​$15 bet on the number 13 or a ​$15 bet that the outcome is any one of the numbers 00, 0, or 1​? ​Why? a. The expected value is ​$nothing. ​(Round to the nearest cent as​ needed.) b. Since the expected value of the bet on the number 13 is ▼   less greater than the expected value for the bet that the outcome is 00, 0, or 1​, the bet on ▼   00, 0, or 1 the single number is better.

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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.