Problem 2. Suppose A and B take turns tossing a biased coin which lands heads with probability p. Suppose A tosses first. Finda) the probability that A tosses the first head;b) the probability that B tosses the first head. Sketch graphs in terms of p.c) Suppose that A tosses once, then B twice, then A once, and so on. Repeat parts a) and b) for this scheme, and find the value of p for which A and B have the same probability of tossing the first head.d) What is B’s chance of tossing the first head for very small values of p? Evaluate this limit as p → 0.
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.
Problem 2. Suppose A and B take turns tossing a biased coin which lands heads with
a) the probability that A tosses the first head;
b) the probability that B tosses the first head. Sketch graphs in terms of p.
c) Suppose that A tosses once, then B twice, then A once, and so on. Repeat parts a) and b) for this scheme, and find the value of p for which A and B have the same probability of tossing the first head.
d) What is B’s chance of tossing the first head for very small values of p? Evaluate this limit as p → 0.
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