Replacements Examples ​​​​(SOA Exam P – Probability – General Probability Module)

In this lesson from the SOA Exam P – Probability module, Professor Stephen Paris explains how to handle replacement and no replacement problems using clear, step-by-step examples. You’ll learn how to: - Differentiate between probability questions with and without replacement. - Apply the correct counting method using combinations and permutations. - Understand how to calculate the probability of drawing specific colors in repeated selections. - Compare two different solution approaches and see why both lead to the same result. Perfect for actuarial students preparing for Exam P, this video helps you strengthen your foundation in combinatorics, probability theory, and counting principles — essential for success on the exam. AnalystPrep Actuarial Exams Study Packages (video lessons, study notes, question bank, and quizzes) can be found at https://analystprep.com/shop/actuarial-exams-complete-courses-by-analystprep/ After completing this video you should be able to: - Calculate probabilities using combinatorics, such as combinations and permutations. Examples given in the video: Example 1: An urn contains 25 red balls, 15 black balls, and 10 green balls. A ball is randomly selected from the urn, its color recorded, and then it’s returned to the urn. This process is repeated 12 times resulting in 5 reds recorded, 4 blacks recorded, and 3 greens recorded. Determine number of distinguishable permutations of the recorded colors. Example 2: An urn contains 25 red balls, 15 black balls, and 10 green balls. A ball is randomly selected from the urn, its color recorded, and then it’s returned to the urn. This process is repeated 12 times. Determine the probability that exactly 5 reds, 4 blacks, and 3 greens are recorded. Example 3: An urn contains 25 red balls, 15 black balls, and 10 green balls. Twelve balls are randomly and simultaneously selected from the urn. Determine the number of ways in which the selection of the 12 balls would result in 5 of them being red, 4 of them being black, and 3 of them being green. Example 4: An urn contains 25 red balls, 15 black balls, and 10 green balls. A ball is randomly selected from the urn, its color recorded, and then it’s returned to the urn. This process is repeated 12 times resulting in 5 reds recorded, 4 blacks recorded, and 3 greens recorded. Determine number of distinguishable permutations of the recorded colors. #ExamP #SOA #ActuarialScience #Probability #Combinatorics #Statistics #StudyTips #AnalystPrep #ActuaryExam #MathLearning