Using wrong total for denominator
"The Total Trouble"
The Mistake in Action
A fair dice is rolled. Find the probability of getting a number greater than 4.
Student writes: "Numbers greater than 4 are 5 and 6. P = 2/4"
Why It Happens
Students correctly identify the favourable outcomes but then use the count of listed outcomes (or some other number) as the denominator instead of the total possible outcomes.
The Fix
Always ask: "How many outcomes are possible in total?"
A dice has 6 faces, so total outcomes = 6.
Favourable outcomes (>4) = 5 and 6 = 2 outcomes
$$P(>4) = \frac{2}{6} = \frac{1}{3}$$
The denominator comes from the original situation, not from your working.
Spot the Mistake
Can you identify where this student went wrong?
Numbers greater than 4: 5, 6
That's 2 numbers
P = 2/4 = 1/2
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: