Andrew, who is planning to retire at age 60, is analyzing various pension options for himself and his spouse, Kim. According to actuarial tables, the probability that Andrew will live for at least 20 years after retiring at age 60 is 63%. Kim will be 57 years old when Andrew retires. The probability that Kim will live for at least 20 years after that is 77%. Assume that the life span of Andrew has no effect on the life span of Kim. (In other words, assume that whether Andrew is alive in 20 years and whether Kim is alive in 20 years are independent events.) a) What is the probability that Andrew does not live for at least 20 years after retiring? b) What is the probability that Kim does not live for at least 20 years after Andrew retires? c) What is the probability that both Andrew and Kim live for at least 20 years after Andrew retires?
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.
Andrew, who is planning to retire at age 60, is analyzing various pension options for himself and his spouse, Kim. According to actuarial tables, the
a) What is the probability that Andrew does not live for at least 20 years after retiring?
b) What is the probability that Kim does not live for at least 20 years after Andrew retires?
c) What is the probability that both Andrew and Kim live for at least 20 years after Andrew retires?
d) What is the probability that neither Andrew nor Kim lives for at least 20 years after Andrew retires?
e) What is the probability that either Andrew or Kim (or both) live for at least 20 years after Andrew retires?
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