To attend a business meeting in Los Angeles, a business traveler based inCincinnati must first fly to Chicago and board a connecting flight. Becauseof the nature of the flights, the traveler has very little time to changeplanes in Chicago. On his way to the airport, he ponders the possibilities.On the basis of past traveling experience, he knows that there is a 70%chance that his plane will be on time in Chicago P(on time inChicago)=0.70. This leaves a 30% chance that his Cincinnati-based planewill arrive late in Chicago. Knowing that if he arrives late, he may not beable to make the connecting flight to Los Angeles, he decides that theprobability that he will be late in Chicago and on time in Los Angeles is20% P(Chicago late and LA on time)=0.20. Suppose that the travelerarrives late in Chicago. Given that he arrived late in Chicago, what is theprobability that he will reach LA on time?
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.
To attend a business meeting in Los Angeles, a business traveler based in
Cincinnati must first fly to Chicago and board a connecting flight. Because
of the nature of the flights, the traveler has very little time to change
planes in Chicago. On his way to the airport, he ponders the possibilities.
On the basis of past traveling experience, he knows that there is a 70%
chance that his plane will be on time in Chicago P(on time in
Chicago)=0.70. This leaves a 30% chance that his Cincinnati-based plane
will arrive late in Chicago. Knowing that if he arrives late, he may not be
able to make the connecting flight to Los Angeles, he decides that the
20% P(Chicago late and LA on time)=0.20. Suppose that the traveler
arrives late in Chicago. Given that he arrived late in Chicago, what is the
probability that he will reach LA on time?
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