Directions: Complete the following questions. The most important part of statistics is the thought process, so make sure that you explain your answers, but be careful with statistics. The following statistics/probability problems may intrigue you and you may be surprised. The answers are not always as you might think. Please answer them as well as you can by using common logic.

1. There are 23 people at a party. Explain what the probability is that any two of them share the same birthday.

2. A cold and flu study is looking at how two different medications work on sore throats and fever. Results are as follows:

• Sore throat - Medication A: Success rate - 90% (101 out of 112 trials were successful)
• Sore throat - Medication B: Success rate - 83% (252 out of 305 trials were successful)

• Fever - Medication A: Success rate - 71% (205 out of 288 trials were successful)
• Fever - Medication B: Success rate - 68% (65 out of 95 trials were successful)

Analyze the data and explain which one would be the better medication for both a sore throat and a fever.

3. The United States employed a statistician to examine damaged planes returning from bombing missions over Germany in World War II. He found that the number of returned planes that had damage to the fuselage was far greater than those that had damage to the engines. His recommendation was to enhance the reinforcement of the engines rather than the fuselages. If damage to the fuselage was far more common, explain why he made this recommendation.