Mohamed Salah is currently the new "blue-eyed boy" of world football. Originally from Egypt but currently playing for Liverpool, his on-field skills have put him in the same league as Lionel Messi and Christiano Ronaldo. Salah has scored 44 goals for the club season so far and many believe that this is just the beginning of a long and illustrious career ahead. Suppose, for a particular match, the probabilities that Salah scores 0, 1, 2 and 3 goals are respectively 0.1, 0.5, 0.3 and 0.1 respectively. On the other hand, his earnings (per match) are tied with the number of goals he scores such that he gets USD 2 million if he does not score any goal while he earns USD 4, 7 and 10 million for scoring 1, 2 and 3 goals respectively. Based on this information, answer the following questions: Find the distribution of Salah's earnings per match along with the mean and standard deviation of the same. i) a. Distribution b. Mean C. Standard deviation ii) Find the probability that Salah earns at least USD 4 million in a particular match.
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.
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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.
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