Some parts of California are particularly earth- quake-prone. Suppose that in one such area, 30% of all homeowners are insured against earth- quake damage. Four homeowners are to be selected at random; let X denote the number among the four who have earthquake insurance. a. Find the probability distribution of X. [Hint: Let S denote a homeowner who has insurance and F one who does not. One possible out- come is SFSS, with probability (.3)(.7)(.3)(.3) and associated X value 3. There are 15 other outcomes.] b. Draw the corresponding probability histogram. c. What is the most likely value for X? d. What is the probability that at least two of the four selected have earthquake insurance?
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.
Some parts of California are particularly earth-
quake-prone. Suppose that in one such area, 30%
of all homeowners are insured against earth-
quake damage. Four homeowners are to be
selected at random; let X denote the number
among the four who have earthquake insurance.
a. Find the
Let S denote a homeowner who has insurance
and F one who does not. One possible out-
come is SFSS, with probability (.3)(.7)(.3)(.3)
and associated X value 3. There are 15 other
outcomes.]
b. Draw the corresponding probability histogram.
c. What is the most likely value for X?
d. What is the probability that at least two of
the four selected have earthquake insurance?
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