To determine whether they have a certain disease, 100 people are to have theirblood tested. However, rather than testing each individual separately, it hasbeen decided first to place the people into groups of 10. The blood samplesof the 10 people in each group will be pooled and analyzed together. If thetest is negative, one test will suffice for the 10 people, whereas if the test ispositive, each of the 10 people will also be individually tested and, in all, 11tests will be made on this group. Assume that the probability that a person hasthe disease is .1 for all people, independently of each other, and compute theexpected number of tests necessary for each group. (Note that we are assumingthat the pooled test will be positive if at least one person in the pool has thedisease.)
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 determine whether they have a certain disease, 100 people are to have their
blood tested. However, rather than testing each individual separately, it has
been decided first to place the people into groups of 10. The blood samples
of the 10 people in each group will be pooled and analyzed together. If the
test is negative, one test will suffice for the 10 people, whereas if the test is
positive, each of the 10 people will also be individually tested and, in all, 11
tests will be made on this group. Assume that the
the disease is .1 for all people, independently of each other, and compute the
expected number of tests necessary for each group. (Note that we are assuming
that the pooled test will be positive if at least one person in the pool has the
disease.)
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