In August 2012, tropical storm Isaac formed in the Caribbean and was headed for the Gulf of Mexico. There was an initial probability of .69 that Isaac would become a hurricane by the time it reached the Gulf of Mexico ( National Hurricane Center website, August 21, 2012). a. What was the probability that Isaac would not become a hurricane but remain a tropical storm when it reached the Gulf of Mexico? b. Two days later, the National Hurricane Center projected the path of Isaac would pass directly over Cuba before reaching the Gulf of Mexico. How did passing over Cuba alter the probability that Isaac would become a hurricane by the time it reached the Gulf of Mexico? Use the following probabilities to answer this question. Hurricanes that reach the Gulf of Mexico have a .08 probability of having passed over Cuba. Tropical storms that reach the Gulf of Mexico have a .20 probability of having passed over Cuba. c. What happens to the probability of becoming a hurricane when a tropical storm passes over a landmass such as Cuba?
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.
In August 2012, tropical storm Isaac formed in the Caribbean and was headed for the
Gulf of Mexico. There was an initial
August 21, 2012).
a. What was the probability that Isaac would not become a hurricane but remain a tropical storm when it reached the Gulf of Mexico?
b. Two days later, the National Hurricane Center projected the path of Isaac would pass
directly over Cuba before reaching the Gulf of Mexico. How did passing over Cuba
alter the probability that Isaac would become a hurricane by the time it reached the
Gulf of Mexico? Use the following probabilities to answer this question. Hurricanes
that reach the Gulf of Mexico have a .08 probability of having passed over Cuba.
Tropical storms that reach the Gulf of Mexico have a .20 probability of having passed
over Cuba.
c. What happens to the probability of becoming a hurricane when a tropical storm passes
over a landmass such as Cuba?
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