In August 2016, a university student was mugged in Jalan Petaling, Kuala Lumpur. In the vicinity of the crime a tall, man with long hair and wearing a black stripe t-shirt are waiting in a silver car. Shortly after the crime was committed, a young, short woman with short and curly hair, was seen running from the scene of the crime and getting into the car, which sped off. The police broadcast a description of the suspected muggers. Soon afterwards, a couple fitting the description was arrested and convicted of the crime. Although the evidence in the case was largely circumstantial, the two peoples were nonetheless convicted of the crime. The prosecutor based his entire case on basic probability theory, showing the unlikeliness of another couple being in that area while having all the same characteristics that the university student described. Table Q4(a) showing the probabilities were used. Table Q4(a) Characteristic Drives silver car Assumed probability 1 out of 14 Man over 6 feet tall 1 out of 6 Man wearing black stripe t-shirt Man with long hair 1 out of 8 I out of 5 1 out of 13 Woman with short hair Woman with curly hair Woman less than 6 feet tall 1 out of 21 1 out of 25 Compute the probability that another couple that was seen in that area has the same characteristic that the university student described. (i) (ii) Based on your answer in Q4(a)(i), suggest the suitable rule to compute the probability; addition or multiplication rule? Based on this case, differentiate the interpretation of addition and multiplication rule.

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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.