Title: “The Great Coin Toss”

Problem: John tosses six fair coins while Mary tosses five. What is the probability that John tosses more heads than Mary.

Materials: Pencil, eleven pennies, paper, calculator.

Math Topic/Concept: Fundamentals of Statistics and Statistical Data

Classroom Use: Developmental

Classroom Use Comments: Pair students up and give each group one penny. Have one person assume the role of John and flip the coin six times. The other person shall assume the role of Mary and flip the coin five times. Have them analyze the outcome if the class repeats this procedure 5-6 times.

Grade: 10-11

Grade Cluster: Early/Late High School

Illinois Goal: 10

Standard: 10.C.4

Source:  “March Problem Calendar”. Mathematics Teacher. Pg. 200-205. March 2001,

Volume 94, Number 3.

Answer: 1/2

Strategies Used: Do a trial run, draw the picture, list the sample space.

Solution: Either John throws more heads than Mary or he doesn’t. Equal number of heads is not possible because John is throwing 1 more coin than Mary. Since there is only two outcomes that are possible, we say that ½ of the time he will throw more heads than Mary.

Extensions or related problems: What is the probability that John tosses more tails than Mary? What is the probability that John and Mary throw equal number of heads and tails?

Intended Rubric:

Write-up Submitted by: Scott Epperly

James R. Olsen, Western Illinois University
E-mail: jr-olsen@wiu.edu
updated: December 16, 2001