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Probability

In this detailed analysis, we explore a probability problem involving genetic predisposition testing. By breaking down the information provided and calculating the values step by step, we aim to find the probability that a randomly selected person who tests positive for a genetic predisposition actually possesses that predisposition. We examine various outcomes, compute products of probabilities, and ultimately arrive at the conclusion that there is a 60% chance that the individual indeed has the predisposition. This example illustrates the importance of understanding conditional probabilities.

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Probability

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  1. Probability Shari carlos Mark shawky Nate stocks

  2. Problem 2.22 • The best way to start this problem is to write out and draw what you’re given. After reading the question once, we know the following information:

  3. Problem 2.22 (cont.) • With the information we’re given, we are able to calculate the rest of the information we are not given. • 1 - .03 = .97 • 1 - .99 = .01 • 1 - .98 = .02 B. C. A.

  4. Problem 2.22 (cont) • Next, we find the product of each possibility by multiplying through each branch. • .03 x .99 = .03 • .03 x .01 – 0.00 • .97 x .02 – 0.02 • .97 x .98 = 0.95

  5. Problem 2.22 • Question: What is the probability that a randomly selected person who tests positive for the predispositionactually has the predisposition? • Here we want to look at 2 different values. We know that 0.03 people test positive for the predisposition, and that (0.03 + 0.02 = 0.05) actually have the predisposition. Therefore: • 0.03 / 0.05 = 60% • Actually have the predisposition

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