Conditional Probability

Question

Total 69 Topics

5 will be chosen randomly

I want to study 20 topics out of 69 topics

what will be the probability that from 20 prepared topics select in randomly in 5

Answer 1

This is a conditional probability problem involving the binomial distribution. We want to find out the probability that exactly 5 of Mary's 20 studied topics are the 5 that appear on the exam. In probability language, given that mary has studied 20 topics, what is the probability that 5 of these will appear on the exam?"

For practice, let's work out the cell sizes for X = 0, 1, 2, 3, 4, 5. The cell for "S" (studied) and "Y" (on the exam) holds the value for X. You work out the other cell values using your knowledge that there are 69 topics total and Mary will study 20 of them. Space permits the inclusion of only X = 0 and X = 1. You will want to do tables for X = 2, 3, 4, and 5

You can calculate a conditional probability as: p(A and B)/p(B). In this case, you will want, X, the number of studied topics on the exam ÷ the number of studied topics, namely 20.