If a hurricane forms in the eastern half of the Gulf of Mexico, there is a 76 percent chance that it will strike the western coast of Florida. From data gathered over the past 50 years, it has been determined that the probability of a hurricane’s occurring in this area in any given year is 0.85. (i) What is the probability that a hurricane will occur in the eastern Gulf of Mexico and strike Florida this year? (ii) If a hurricane in the eastern Gulf of Mexico is seeded (induced to rain by addition of chemicals from aircraft), its probability of striking Florida’s west coast is reduced by one-fourth. If it is decided to seed any hurricane in the eastern gulf, what is the new value for the probability in part (a)?
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.
If a hurricane forms in the eastern half of the Gulf of Mexico, there is a 76 percent
chance that it will strike the western coast of Florida. From data gathered over the
past 50 years, it has been determined that the
this area in any given year is 0.85.
(i) What is the probability that a hurricane will occur in the eastern Gulf of Mexico
and strike Florida this year?
(ii) If a hurricane in the eastern Gulf of Mexico is seeded (induced to rain by addition
of chemicals from aircraft), its probability of striking Florida’s west coast is
reduced by one-fourth. If it is decided to seed any hurricane in the eastern gulf,
what is the new value for the probability in part (a)?
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