Question

5. Twenty-five sixth-grade students entered a math contest consisting of 20 questions. The student who

answered the greatest number of questions correctly will receive a graphing calculator. The rules of the
contest state that if two or more students tie for the greatest number of correct answers, one of these
students will be chosen to receive the calculator.
No student answered all 20 questions correctly, but four students (Allan, Beth, Carlos, and Denesha) each
answered 19 questions correctly.
What would be a fair way to use two coins (a dime and a nickel) to decide which student should get the
calculator? Explain what makes your method fair.

Answer 1

two coins are flipped:

• if dime land heads and nickel land heads then Allan wins

• if dime land heads and nickel land tail then Beth wins

• if dime land tail and nickel land heads then Carlos wins

• if dime land tail and nickel land tail then Denesha wins

Explanation:

The method described above is fair since the probability of each case is 0.25.

If the two coins are flipped:

• The probability dime land head is 0.5

• The probability dime land tail is 0.5

• The probability nickel land head is 0.5

• The probability nickel land tail is 0.5

Then the probability dime land heads and nickel land heads is 0.5 × 0.5 = 0.25.

The other four cases are calculated similarly and their probability is also 0.25