Introductory Probability requires multivariable calculus (e.g., Math 200) as a prerequisite and is much more mathematical than an introductory statistics course. Introductory Statistics courses involve data analysis and statistical software, whereas Introductory probability courses do not.
Here's an example of an exam question in introductory Probability:
An insurance policy pays a total medical benefit consisting of two parts for each claim. Let X represent the part of the benefit that is paid to the surgeon, and let Y represent the part that is paid to the hospital. The variance of X is 4000, the variance of Y is 8000, and the variance of the total benefit, X+Y, is 14000.
(a) What is the covariance of X and Y?
(b) Due to increasing medical costs, the insurance company decides to increase X by a flat amount of 100 per claim and to increase Y by 10% per claim. Calculate the variance of the total benefit after these revisions have been made.
Here's an example of an exam question in introductory Statistics:
Physical fitness testing is an important aspect of athletic training. A common measure of the magnitude of cardiovascular fitness is the maximum volume of oxygen uptake during a strenuous exercise. A study was conducted on 24 middle-aged men to study the influence of the time that it takes to complete a 3 km run on the oxygen uptake. The scatter diagram of oxygen uptake against time is roughly oval-shaped. The regression analysis for the data is summarized as [... not repeated here].
(a) Predict the maximum volume of oxygen intake, when the time takes to complete 3 km run is (i) 700 seconds and (ii) 1120 seconds.
(b) Does the time it takes to run a distance of 3 km have a significant influence on maximum oxygen intakes? (Answer with yes or no and explain in no more than 20 words.)