During the coronavirus disease 2019 (COVID19) crisis, there has been a public outcry for mass screening of the population in hopes to control an actively unfolding event. To this date, there is one test that has assisted in the current crisis, real-time reverse transcriptase-polymerase chain reaction (rRT-PCR). Although becoming more readily available, there are shortcomings to the test when placed in real-world situations. The probability that the rRT-PCR correctly identifies someone with COVID as positive is 0.87, and the probability that the test incorrectly identifies someone without COVID as positive is 0.01. The incidence of COVID in the general population is 0.001. You take the test, and the result is positive. Let P denote the event that you have COVID. Let R denote the event that the rRT-PCR result is positive. a) What is the equivalent mathematical notation for 0.87? b) What is the equivalent mathematical notation for 0.01? c) What is the equivalent mathematical notation for 0.001?
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.
During the coronavirus disease 2019 (COVID19) crisis, there has been a public outcry for mass screening of the population in hopes to control an actively unfolding event. To this date, there is one test that has assisted in the current crisis, real-time reverse transcriptase-polymerase chain reaction (rRT-PCR). Although becoming more readily available, there are shortcomings to the test when placed in real-world situations. The probability that the rRT-PCR correctly identifies someone with COVID as positive is 0.87, and the probability that the test incorrectly identifies someone without COVID as positive is 0.01. The incidence of COVID in the general population is 0.001. You take the test, and the result is positive. Let P denote the event that you have COVID. Let R denote the event that the rRT-PCR result is positive.
a) What is the equivalent mathematical notation for 0.87?
b) What is the equivalent mathematical notation for 0.01?
c) What is the equivalent mathematical notation for 0.001?
d)What is the value of P(R)?
e)What is the probability that you have the COVID?
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