Probability and Statistics

Probability

Calculating Probability

Addition Rule of Probability and Expected Frequency

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Absolute Frequency and Relative Frequency

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Median, Mean, Mode, Range from a Frequency Table

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Addition Rule of Probability and Expected Frequency

Probability and Statistics Addition Rule of Probability and Expected Frequency

Courses Overview

🎬 Video Tutorial

(0:01) What are Equiprobable Events? Equiprobable events are events with equal chances of occurring. For example, when rolling a fair six-sided die, each face has a probability of $\frac{1}{6}$ of landing face-up.
(0:25) How to Calculate the Probability of Single Events? Probability is found by dividing the number of favourable outcomes by the total number of possible outcomes. For example, if a bag contains 50 balls (25 blue, 15 red, and 10 yellow), the probability of randomly drawing a blue ball is $ \frac{25}{50} = 50\text{%} $, and the probability of drawing a red ball is $ \frac{15}{50} = 30\text{%} $.
(1:32) What is the Addition Rule of Probability? When events are mutually exclusive (meaning they cannot happen at the same time), the probability of $A$ or $B$ is the sum of their individual probabilities. For example, the probability of drawing a blue or red ball is $ P(\text{Blue or Red}) = P(\text{Blue}) + P(\text{Red})$ = $50\text{%} + 30\text{%} = 80\text{%} $.
(2:23) Understanding Expected Frequency: Expected absolute frequency tells us how often we expect an event to occur over a number of trials. For example, when rolling a fair six-sided die $60$ times, the probability of rolling a 3 is $ \frac{1}{6} $, so the expected frequency is $ \left( \frac{1}{6} \right) \times 60 = 10 $ times. However, since “expected” is just an estimation, actual results may vary.

📂 Revision Cards

Explanation of equiprobable events by using a die and showing that each face has an equal probability of 1/6. — 1) What are Equiprobable Events?

Drawing coloured balls from a bag with 50 balls, showing 50% for blue and 30% for red. — 2) Calculating Probability of Single Events

Explanation of the probability of drawing blue or red balls from a bag with 50 balls using the addition rule of probability for mutually exclusive events. — 3) Addition Rule of Probability

Calculating the expected absolute frequency using a die, illustrating that the expected absolute frequency of rolling a "3" over 60 trials is 10. — 4) Expected Absolute Frequency

🍪 Quiz

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Probability Rules and Expected Values

1 / 6

Q: 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?

$\frac{3}{5}$

$\frac{2}{5}$

$\frac{1}{5}$

$\frac{35}{50}$

Feedback: Not quite! There are 10 yellow balls out of a total of 50. The probability of drawing a yellow ball is $\frac{10}{50}$, which simplifies to $\frac{1}{5}$.

Feedback: Well done! There are 10 yellow balls out of a total of 50. The probability of drawing a yellow ball is $\frac{10}{50}$, which simplifies to $\frac{1}{5}$.

2 / 6

Q: If you roll a fair six-sided die, what is the probability of rolling either a 2 or a 6?

$\frac{1}{3}$

$\frac{1}{2}$

$\frac{1}{6}$

$\frac{6}{6}$

Feedback: Not quite! There are two favourable outcomes (rolling a 2 or a 6) out of 6 possible outcomes. Therefore, the probability is $\frac{2}{6}$, which simplifies to $\frac{1}{3}$.

Feedback: Well done! There are two favourable outcomes (rolling a 2 or a 6) out of 6 possible outcomes. Therefore, the probability is $\frac{2}{6}$, which simplifies to $\frac{1}{3}$.

3 / 6

Q: A box contains 15 red, 5 blue, and 10 green marbles. What is the probability of drawing a red or green marble?

$\frac{5}{6}$

$\frac{1}{2}$

$\frac{1}{6}$

$\frac{1}{3}$

Feedback: Not quite! The total number of red and green marbles is 15 (red) + 10 (green) = 25 marbles. The total number of marbles is 30. The probability of drawing a red or green marble is $\frac{25}{30}$, which simplifies to $\frac{5}{6}$.

Feedback: Well done! The total number of red and green marbles is 15 (red) + 10 (green) = 25 marbles. The total number of marbles is 30. The probability of drawing a red or green marble is $\frac{25}{30}$, which simplifies to $\frac{5}{6}$.

4 / 6

Q: A bag contains 6 red, 4 blue, and 2 yellow marbles. What is the probability of drawing a yellow or blue marble?

$\frac{1}{2}$

$\frac{5}{12}$

$\frac{2}{3}$

$\frac{10}{12}$

Feedback: Not quite! The total number of yellow and blue marbles is 4 (blue) + 2 (yellow) = 6 marbles. The total number of marbles is 12. So, the probability of drawing a yellow or blue marble is $\frac{6}{12}$, which simplifies to $\frac{1}{2}$.

Feedback: Well done! The total number of yellow and blue marbles is 4 (blue) + 2 (yellow) = 6 marbles. The total number of marbles is 12. So, the probability of drawing a yellow or blue marble is $\frac{6}{12}$, which simplifies to $\frac{1}{2}$.

5 / 6

Q: You roll a fair die 60 times. How many times would you expect to roll a 3?

15

12

18

10

Feedback: Not quite! The probability of rolling a 3 on a fair die is $\frac{1}{6}$. If you roll the die 60 times, the expected number of 3s is $\frac{1}{6} \times 60 = 10$.

Feedback: Well done! The probability of rolling a 3 on a fair die is $\frac{1}{6}$. If you roll the die 60 times, the expected number of 3s is $\frac{1}{6} \times 60 = 10$.

6 / 6

Q: You roll a fair die 120 times. How many times would you expect to roll a number less than 3?

40

60

20

80

Feedback: Not quite! The probability of rolling a number less than 3 (either 1 or 2) is $\frac{2}{6}$, which simplifies to $\frac{1}{3}$. So if you roll the die 120 times, you would expect $\frac{1}{3} \times 120 = 40$ rolls to be less than 3. Note that this is an estimate, the actual number might be a bit higher or lower.

Feedback: Well done! The probability of rolling a number less than 3 (either 1 or 2) is $\frac{2}{6}$, which simplifies to $\frac{1}{3}$. So if you roll the die 120 times, you would expect $\frac{1}{3} \times 120 = 40$ rolls to be less than 3. Note that this is an estimate, the actual number might be a bit higher or lower.

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