What Is Indicated Probability?
The indicated probability is the probability of the event you name, such as drawing a red or a blue marble. It equals the number of favourable outcomes divided by the total number of outcomes.
Enter each outcome with its count, then list the outcomes in your event. The calculator gives the probability as a decimal, fraction and percentage, the complement, the odds in favour and a chart that highlights your event.
Below are the formulas, a worked marble example and answers on combining outcomes.
How to Use the Indicated Probability Calculator
- List each outcome with its count.
- Name the outcome or outcomes in your event.
- Read the probability.
- Check the outcome table.
Indicated Probability Formula
Probability
Complement
Indicated Probability Variables Explained
| Symbol | Meaning | Notes |
|---|---|---|
| P(E) | Probability of the event | |
| Favourable | Outcomes in the event | |
| Total | All outcomes | |
| Odds | Favourable to other |
Indicated Probability Worked Example
A bag holds 5 red, 3 blue, 2 green and 4 yellow marbles, 14 in all. The probability of red or blue is (5 + 3) ÷ 14 = 8/14 = 4/7 ≈ 0.5714. The odds in favour are 8 to 6, which is 4 to 3.
With the example values loaded in the calculator above, the steps are:
- Total outcomes = 5 + 3 + 2 + 4 = 14.
- Favourable outcomes (Red or Blue) = 8.
- P(event) = favourable ÷ total = 8 ÷ 14 = 0.57142857.
- P(not event) = 1 − 0.57142857 = 0.42857143.
Result: P(indicated event) = 0.57142857; As a fraction = 4 / 7.
How to Read an Indicated Probability
A probability runs from 0 to 1. A value of 0 means the event cannot happen, and a value of 1 means it is certain. For the bag with 5 red, 3 blue, 2 green and 4 yellow marbles, the chance of red or blue is 8 ÷ 14, which is about 0.571, or roughly 57%.
Odds are a different scale. Odds in favour compare the event with its opposite: 8 favourable to 6 unfavourable, or 4 to 3. Probability 4/7 and odds 4:3 describe the same chance, so do not mix them in one sentence.
Where Indicated Probability Is Used
Counting problems
Enter the favourable and total outcomes, or list outcomes with their counts, to get the probability as a fraction, a percentage and a decimal.
Either-or events
Add the counts when the events cannot happen together, such as drawing a red or a blue marble. List each outcome with its count to get the combined probability.
Odds and bets
Convert a probability to odds in favour and against, which is the form used in gambling and some textbooks.
Checking homework
Compare your fraction and your decimal with the calculator, and confirm that the probabilities of all outcomes add to 1.
Common Indicated Probability Mistakes to Avoid
- Count outcomes in the whole sample space first. Leaving one out makes every probability too high.
- Add probabilities for "or" only when the events cannot happen together. Otherwise subtract the overlap.
- Do not confuse odds with probability. Odds of 4 to 3 equal a probability of 4/7, not 4/3.
- Simplify the fraction at the end, but keep the decimal to four places for comparison.
Indicated Probability Terms and Definitions
- Event
- A set of outcomes you are interested in.
Indicated Probability FAQs
How do I find the probability of an indicated event?
Divide the number of outcomes in the event by the total number of equally likely outcomes. If a bag has 5 red marbles out of 14, P(red) = 5 ÷ 14 ≈ 0.357.
How do I find the probability of one outcome or another?
If the two outcomes cannot happen together, add their probabilities. For red or blue in the 14-marble bag that is (5 + 3) ÷ 14 = 8/14 = 4/7. If they can overlap, subtract the probability that both happen.
What are the odds in favour?
Odds in favour are the favourable outcomes against the unfavourable ones. With 8 favourable and 6 unfavourable outcomes, the odds are 8 to 6, which simplifies to 4 to 3.
What is the probability of the opposite event?
It is 1 minus the probability of the event. If P(red or blue) = 4/7, the chance of green or yellow is 1 − 4/7 = 3/7. This complement rule is often the quickest route to "at least one" problems.