Statistics Question

Question

1. There are 23 people at a party. Explain what the probability is that any two of them share the same birthday.
6.3%




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.

Answer 1

1.  This is a classic probability problem. The probability of there being at least one duplicate date-of-birth (year & month only) in a room of randomly selected persons (perhaps with twins refused admission) is about 0.5 for n = 22 persons in the room, and this probability increases as n increases.  Counter-intuitive, but true.

 

I have tested this in many classrooms throughout the years, and often students have been stunned that when we had only 20 or so students, a match occurred.  One year, it happened TWICE to me that the first coincidence discovered was my own DOB, November 1.