Anticipated Student Response for Probability Open-Ended Problem

EXAMPLE 3

This tree diagram shows the possible results of guessing on a 5-question T/F quiz.  In the diagram “C” stands for correct answers and “W” stands for wrong answers.  I chose to focus on correct and wrong answers, rather than true and false, because it gives a better view of the grade received in each possible way to answer the quiz.  To find the mathematical probability, I counted all the branches, representing the total number of ways to answer the quiz.  This total of 32 represents the sample space and should be used in the denominator of the probability calculation.  To find the numerator, or the number of ways to pass the test, I simply looked for the branches with only 1 or 0 W’s, because that would mean the student scored either 80% for missing 1 or 100% for missing 0.  I found 6 ways to pass the test.  This means that the mathematical probability would be 6/32 or 19% or .19.  This means that almost 20% or 2 students out of 10 would pass the quiz.

            This tree diagram could also be used to find how many ways a family of 5 could have boys and girls.  This solution on passing the test would relate to having either all of one sex (choose one) or 4 of one sex and 1 of the other.  For example, the probability that a family would have no boys or only 1 boy is the same as the probability of passing a 5—question T/F quiz.  Out of the 32 possible outcomes, 1 way shows all girls and 5 ways show having only 1 boy and 4 girls.  The mathematical probability of a family of 5 having 1 or 0 boys is 6/32 or 19% or .19.  The inverse of this condition, having only 1 girl and 4 boys or having 0 girls and 5 boys, would have the identical mathematical probability, because in the chart below you could substitute “girls” for “correct” and “boys” for “wrong” or you could substitute “boys” for “correct” and “girls” for “wrong.”  

See the entire Probability Lesson Plan

Created by Alice Gabbard