Q3 what is the probability that you will get two

This preview shows page 2 - 5 out of 7 pages.

Q3: What is the probability that you will get two heads on flips three and four, conditional on getting two heads on flips one and two? A3: Probability of two heads on p (F3&4) conditional on two heads for p(F1&2). Using Bayes Theorem, we determine that it is not very useful in this form. Here, we are looking for the probability of the second item, p (F3&4), given the first, p (F1&2). The vertical bar means “given.” Which still is not very helpful. We did not calculate it this way. We did not calculate p (F1&2|F3&4). If we had, we would know the answer is just 1 minus the result. But we did calculate each part’s relation to the whole. So use the form of Bayes’ theorem that uses the law of total probability as the denominator : Which is p (F3&4)’s proportion to the total probability. From the table we made, we already know all of those pieces on the right-hand side: Example Problem Interpretation: The conditional probability that you will flip two heads in a row after previously flipping two heads in a row is 50%. Bear in mind that the raw probability of flipping two
heads in a row in independent trials is 25% and flipping four heads in a row in independent trials is 6.25%.
Recap of the Method Used in Example Problem: 1. Define success of an individual trial. 2. Use the binomial equation to calculate the cumulative probability of each part of the system. 3. Make a table with each part’s p and its percentage contribution to the whole. The percentages must add to 1. 4. Calculate the p (Total) using the law of total probability. 5. Use the total probability form of Bayes’ theorem to calculate the conditional probability for the item of interest. 6. Interpret. Homework Problems: Using the example problem as reference, complete the following five problems. Turn in the work and results for each of the five problems. (Note: 4 includes a,b,c and 5 includes a,b,c,d). Note that each problem provides a hint which should guide you through the problem along with the Example Problem as a reference. Post any questions you have to the General Discussion area. Problem 1: You are taking a 10 question multiple choice test. If each question has four choices and you guess on each question, what is the probability of getting one question correct? [Hint: This is a binomial in the form of 10 choose 1 with p=.25.] =

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture