A study of drug offenders who have been treated for drug abuse suggests that the chance of conviction within a 2-year period after treatment may depend on the offender's education. The proportions of the total number of cases that fall into four education/conviction categories are shown in the following table. Status Within 2 Years After Treatment Education Convicted Not Convicted Totals 10 Years or More 0.11 0.29 0.40 9 Years or Less 0.26 0.34 0.60 Totals 0.37 0.63 1.00 Suppose a single offender is selected from the treatment program. Here are the events of interest. A: The offender has 10 or more years of education B: The offender is convicted within 2 years after completion of treatment Find the appropriate probabilities for these events. (Round your answers to three decimal places.) (a) A Answer:_________________ (b) B Answer:_________________ (c) A ∩ B Answer:_________________ (d) A ∪ B Answer:_________________ (e) AC Answer:_________________ (f) A given that B has occurred Answer:_________________ (g) B given that A has occurred Answer:_________________
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
Tree diagram
Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
| Status Within 2 Years After Treatment |
|||
|---|---|---|---|
| Education | Convicted | Not Convicted |
Totals |
| 10 Years or More | 0.11 | 0.29 | 0.40 |
| 9 Years or Less | 0.26 | 0.34 | 0.60 |
| Totals | 0.37 | 0.63 | 1.00 |
| A: | The offender has 10 or more years of education |
| B: | The offender is convicted within 2 years after completion of treatment |
Trending now
This is a popular solution!
Step by step
Solved in 4 steps
