Addition Rule of Probability and Expected Frequency
The addition rule of probability finds the chance of A or B when they are mutually exclusive (cannot both happen). Just add: P(A or B) = P(A) + P(B). Expected frequency is how often it happens: probability × number of trials.
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What Are Equiprobable Events?
- Equiprobable events are events with the same chance of happening.
- When rolling a fair die, each number has an equal probability of 1/6.
Calculating Probability: Single Event
- Probability equals number of favourable outcomes ÷ total outcomes.
- For example, drawing a blue ball from 50 balls with 25 blue gives .
Probability of “OR” Events
- Use OR when either event can happen.
- Add the favourable outcomes for each event, then divide by the total outcomes.
Addition Rule for Probability
- Mutually exclusive events cannot happen at the same time.
- For example, a ball cannot be red and blue at the same time.
- When events are mutually exclusive, use P(A or .
Expected Absolute Frequency
- Expected absolute frequency is how often an event is expected to happen.
- It equals probability × number of trials.
- It is an estimate, so what actually happens can vary.
Practice Questions
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In a bag with 50 balls, there are 25 blue, 15 red, and 10 yellow balls. What is the probability of drawing a yellow ball?
Correct! 🎉 +10 pointsNot quite right
There are 10 yellow balls out of a total of 50. The probability of drawing a yellow ball is , which simplifies to .
If you roll a fair six-sided die, what is the probability of rolling either a 2 or a 6?
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There are two favourable outcomes (rolling a 2 or a 6) out of 6 possible outcomes. The probability is , which simplifies to .
A box contains 15 red, 5 blue, and 10 green marbles. What is the probability of drawing a red or green marble?
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The number of red and green marbles is . The total number of marbles is 30. The probability is , which simplifies to .
A bag contains 6 red, 4 blue, and 2 yellow marbles. What is the probability of drawing a yellow or blue marble?
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The number of yellow and blue marbles is . The total number of marbles is 12. The probability is , which simplifies to .
You roll a fair die 60 times. How many times would you expect to roll a 3?
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The probability of rolling a 3 on a fair die is . Over 60 rolls, the expected number of times is .
You roll a fair die 120 times. How many times would you expect to roll a number less than 3?
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The numbers less than 3 are 1 and 2, giving a probability of , which simplifies to . Over 120 rolls, the expected number is .
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Addition rule of probability
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Students Also Ask
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Mutually exclusive means two events cannot happen at the same time. If one event occurs, the other is impossible. For example, when picking a single ball from a bag, it cannot be both blue and red. You must confirm events are mutually exclusive before using the addition rule of probability.
A bag contains 50 balls: 25 blue, 15 red, and 10 yellow. The probability of picking a blue or red ball equals P(blue) + P(red), which is 0.5 + 0.3 = 0.8. This works because picking blue and picking red are mutually exclusive events that cannot happen at the same time.
Expected frequency is a prediction based on probability, not a guaranteed outcome. If you roll a fair die 60 times, you would expect to roll a 3 about 10 times. In practice, you may get fewer, the same, or more than 10. Each roll is an independent event with its own outcome.
Expected frequency is the number of times you predict an event will happen, calculated using probability and the number of trials. Actual frequency is the number of times the event really does happen when you carry out the experiment. The two values may differ because probability gives an estimate, not an exact result.
In probability, "or" means you want the chance of one event or another happening. For mutually exclusive events, you add their individual probabilities together. For example, P(blue or red) equals P(blue) plus P(red). The addition rule of probability applies whenever you see "or" between mutually exclusive events.