An engineering construction firm is currently workingon power plants at three different sites. Let Ai denotethe event that the plant at site i is completed by thecontract date. Use the operations of union, intersection,and complementation to describe each of thefollowing events in terms of A1, A2, and A3, draw aVenn diagram, and shade the region corresponding toeach one.a. At least one plant is completed by the contractdate.b. All plants are completed by the contract date.c. Only the plant at site 1 is completed by the contract date.d. Exactly one plant is completed by the contract date.e. Either the plant at site 1 or both of the other twoplants are completed by the contract date.
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.
An engineering construction firm is currently working
on power plants at three different sites. Let Ai denote
the
contract date. Use the operations of union, intersection,
and complementation to describe each of the
following events in terms of A1, A2, and A3, draw a
Venn diagram, and shade the region corresponding to
each one.
a. At least one plant is completed by the contract
date.
b. All plants are completed by the contract date.
c. Only the plant at site 1 is completed by the contract date.
d. Exactly one plant is completed by the contract date.
e. Either the plant at site 1 or both of the other two
plants are completed by the contract date.
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