The National Hurricane Center said it's monitoring a weather system (Hurricane Irma), which is currently producing showers and thunderstorms in the southwestern Gulf of Mexico. Residents along the Gulf and East coasts of the U.S. need to be on alert. As shown in the figure, the exact path of Irma remains uncertain and will depend on a variety of moving parts in the atmosphere. In the first scenario (scenario A), Irma will blast the northern Caribbean with flooding rain, damaging winds and rough surf this week, bringing life-threatening conditions to the islands. According to the forest, the probability that scenario A occurs is P(A)=0.4. A similar scenario (scenario B) could play out somewhere along the Gulf or East coasts this weekend or next week. According to the forest, the probability that scenario B occurs is P(B)=0.45. Another scenario (scenario C) still on the table is that Irma curves northward and misses the East Coast entirely. However, this scenario is the least likely to occur at this point with a probability P(C)=0.15. Let F denote the “flooding event in Miami area caused by Hurricane Irma”, and assume that P(F|A)=0.4, P(F|B)=0.9, and P(F|C)=0.1, answer the following questions. What is the probability that there will be a flooding event in Miami area caused by Hurricane Irma? a). 0.58 b). 0.16 c). 0.405 d). 0.015 e). none of above If Miami is flooded, what is the probability that Hurricane Irma takes trajectory B? a). 0.7 b). 0.45 c). 0.6 d). 0.28 e). none of abo
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
The National Hurricane Center said it's monitoring a weather system (Hurricane Irma), which is currently producing showers and thunderstorms in the southwestern Gulf of Mexico. Residents along the Gulf and East coasts of the U.S. need to be on alert. As shown in the figure, the exact path of Irma remains uncertain and will depend on a variety of moving parts in the atmosphere. In the first scenario (scenario A), Irma will blast the northern Caribbean with flooding rain, damaging winds and rough surf this week, bringing life-threatening conditions to the islands. According to the forest, the probability that scenario A occurs is P(A)=0.4. A similar scenario (scenario B) could play out somewhere along the Gulf or East coasts this weekend or next week. According to the forest, the probability that scenario B occurs is P(B)=0.45. Another scenario (scenario C) still on the table is that Irma curves northward and misses the East Coast entirely. However, this scenario is the least likely to occur at this point with a probability P(C)=0.15. Let F denote the “flooding
What is the probability that there will be a flooding event in Miami area caused by Hurricane Irma?
a). 0.58 b). 0.16 c). 0.405 d). 0.015 e). none of above
If Miami is flooded, what is the probability that Hurricane Irma takes trajectory B?
a). 0.7 b). 0.45 c). 0.6 d). 0.28 e). none of above
Here Bayes theorem is applicable
P(A|B) =
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