Three coin problem

Introduction

This page includes the three coins problem.

Coin sides:

  1. red - red;
  2. red - blue; &
  3. blue- blue

And the problem asks for the probability of a particular situation:

If one of the three coins is selected and placed on a table so it can be seen that the top is red, what is the probability the other side is red?

Below is an explanation, instructional suggestions, and worksheet to share with others and use in classrooms.

Three red & blue coins (red - red; red - blue; & blue- blue)

Pedagogical suggeestions

Review the three red and blue coin challenge.

Review theoretical probability.

Probability can be determined theoretically, by reasoning to find the total possible outcomes, the total of each specific outcome, and the proportion of the specific outcomes to the total.

In this problem some people believe the probability is one in two (1:2) or 50:50.

They reason since the coin has a red side then the coin two blue sides isn't possible, and that leaves the two other coins, hence 1:2.

However, and this is tricky so take it easy as you review the following to determine the total possible outcomes.

Discussion:

There are six sides that could be seen: red, red, blue, blue, red, blue.

  1. RR - 2 sides
  2. BB - 2 sides
  3. RB - 2 sides

Six sides.

If it is known that the side showing is red, that eliminates the BB coin as selected.

That leaves two coins RR or RB as the remaining sides: R, B, R, R

However, you have a red side showing, so that leaves three sides that might not be showing: B, R, R

You know for the RB coin the

1. R side is showing and Blue side woud be hidden

Or for the RR coin the

2. Red side top could be showing; Red side bottom not showing;

3. Red side top showing; Red side bottom not showing

Thus out of the three possibilities outcomes, how many of the possible sides could be hidden and red?

 

 

Three red & blue coins (red - red; red - blue; & blue- blue)

Challenge

You have a set of three coins.

  1. One is red on both sides
  2. Another is blue on both sides
  3. The last is red on one side and blue on the other.

If one of the three coins is selected and placed on a table so it can be seen that the top is red, what is the probability the other side is red?

Set up

 

Three coins Red blue coins

Work space.

 

 

 

 

 

 

 

 

 

 

 

 

Hint:

List the color of each of side of all three coins.

Use that to act out the problem and the possibilities.