A reliable method
Use one minus a probability to find its complement. For drawing without replacement, update the total and the category counts before calculating the second probability.
The common trap
Independent events and mutually exclusive events mean different things. Independent probabilities can be multiplied; mutually exclusive outcomes cannot occur together.
Check and transfer
Check that a probability lies between zero and one, and explain the denominator in words. If the denominator is unclear, the sample space probably needs revision.
Worked comparison: why the alternative fails
A bag has 4 red and 3 blue tokens. After one red is removed, P(blue next)=3/6=1/2. Using 3/7 retains the old total; using 2/6 removes the wrong color. State which counts changed before forming the fraction.
Transfer and explain
For independent events with probabilities 1/3 and 1/4, both occur with probability 1/12. Adding gives 7/12, which does not represent the joint independent outcome.
A bag has 4 green and 8 purple tokens. Each token is equally likely to be chosen. What is the probability of green?
- Count all tokens to define the equally likely outcomes.
- Divide the green-token count by the total.
- The requested value is 1/3. Check its units and meaning against the original question.
Compare the other answer choices
Count only one green token as favorable.
Use purple rather than green as the favorable category.
Divide green by purple instead of by the whole bag.
Try it, then explain it.
Complete a short set without looking at the example. After each answer, explain which operation preserved the relationship and why the result makes sense.
Sources & authorship
Original Slope explanations and examples. References support the concepts; they are not the source of copied questions. Independent educator review is pending.
GED Mathematical Reasoning overviewSiyavula Grade 10 mathematics foundation reference