1. Warm Up
Doctors often try to predict the gender of a baby based on ultrasound images. Data on these predictions is shown. Predicted Male Predicted Female Is Male Is Female ) What is the probability the prediction is correct? 2) If the baby is predicted male, what is the probability it is male? 3) If the baby is predicted female, what is the probability it is female?

2. Example Data Set
A 2016 study from the Pew Research Center found the percent of U.S. adult internet users within the given age groups who have a Twitter account. Age Group % of All Adults % on Twitter

3. Who Made the Shot?
Kevin Durant and Dr. Lutze are hanging around the gym one day with you. You look away for a moment and hear a shot swish through the net. When you look back both K.D. and Dr. Lutze claim they made the shot. Being an expert statistician you know the following: P(K.D. makes a shot) = 0.6 P(Dr. Lutze makes a shot) = 0.3 P(K.D. takes a shot) = 0.75 P(Dr. Lutze takes a shot) = 0.25 What is the probability Dr. Lutze took the shot?

4. Cancer Screening
A test for a certain type of cancer is 98% accurate. If you have this cancer, the test is positive (indicates cancer) 98% of time. If you don’t have this cancer, the test is negative (indicates no cancer) 98% of time. Only 0.5% of the population has this type of cancer. Your doctor tells you the test results are positive. What is the probability you actually have cancer?

5. Additional Practice
A tennis tournament with 4 players will be held. In the first round Seed #1 plays Seed #4 and Seed #2 plays Seed #3. The winners meet in the championship. Suppose the following probabilities are known: P(Seed #1 beats Seed #4) = 0.8 P(Seed #1 beats Seed #3) = 0.7 P(Seed #1 beats Seed #2) = 0.6 P(Seed #2 beats Seed #4) = 0.7 P(Seed #2 beats Seed #3) = 0.6 P(Seed #3 beats Seed #4) = 0.6 What is the probability that Seed #1 will win the tournament?