Refer to the contingency table shown below. Smoking by Race for Males Aged 18-24 Smoker (S) Nonsmoker (N) Row Total White (W) 289 571 860 Black (B) 50 90 140 Column Total 339 661 1,000 Click here for the Excel Data File (a) Calculate the probabilities given below: (Round your answers to 4 decimal places.) i. P(S) ii. P(W) iii. P(S | W) iv. P(S | B) v. P(S and W) vi. P(N and B) (b) Do you see evidence that smoking and race are not independent? Yes No (c) Why might public health officials be interested in this type of data? Health officials might target or design special programs based on race. Health officials can use this as an excuse to explain the lack of initiatives to curb smoking. Health officials are not interested.
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.
Refer to the
| Smoking by Race for Males Aged 18-24 | |||||||||
| Smoker (S) |
Nonsmoker (N) |
Row Total | |||||||
| White (W) | 289 | 571 | 860 | ||||||
| Black (B) | 50 | 90 | 140 | ||||||
| Column Total | 339 | 661 | 1,000 | ||||||
Click here for the Excel Data File
(a) Calculate the
| i. | P(S) | ||
| ii. | P(W) | ||
| iii. | P(S | W) | ||
| iv. | P(S | B) | ||
| v. | P(S and W) | ||
| vi. | P(N and B) | ||
(b) Do you see evidence that smoking and race are not independent?
-
Yes
-
No
(c) Why might public health officials be interested in this type of data?
-
Health officials might target or design special programs based on race.
-
Health officials can use this as an excuse to explain the lack of initiatives to curb smoking.
-
Health officials are not interested.
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