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22/09/25

Learning Objective

7MPS5: Applying mathematical strategies to solve problems involving statistics

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15/09/25

Learning Objective

6MPSE1: To estimate and represent the chance or likelihood of a random event using simple fractions, decimals or percentages

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Draw your own spinner divided into 12 sections with different colours. Calculate the probability for each colour, and try to create a rule where landing on green wins. Determine the frequency it needs to win reliably.

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You have a deck of cards with 52 cards: 26 red cards (hearts and diamonds) and 26 black cards (clubs and spades).

1. What is the probability of drawing a red card from the deck? Express your answer as a fraction, decimal, and percentage.

2. If you draw 20 cards from the deck, how many red cards would you expect to draw? Explain your reasoning.

3. Imagine you add 10 more red cards to the deck. How would this change the probability of drawing a red card? Calculate the new probabilities.

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Design an intricate probability game using combinations of dice, coins, and spinners. Set different winning conditions and calculate the probability for each scenario, expressing them in fractions, decimals, and percentages.

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You have a box of 30 chocolates: 10 are dark chocolate, 12 are milk chocolate, and 8 are white chocolate.

1. What is the probability of randomly selecting each type of chocolate? Provide your answers as fractions, decimals, and percentages.

2. If you randomly pick 15 chocolates from the box, how many of each type would you expect to get? Explain your reasoning and show your work.

3. If you could add one more type of chocolate to the box, what would it be? How would that change the probabilities for selecting each type?

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Research the probability of different weather conditions affecting Hong Kong. Discuss how these are calculated and compare them across seasons, presenting findings in fractions, decimals, and percentages.

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Imagine you have a bag with 20 marbles: 5 red, 7 blue, and 8 green. You randomly pick one marble from the bag without looking.

1. What is the chance of picking a red marble? Express your answer as a fraction, decimal, and percentage.

2. If you were to pick a marble 10 times, how many red marbles would you expect to pick? Explain your reasoning.

3. What other questions could you ask about the chances of picking different colors of marbles from the bag?

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1. Rolling the Dice:

Roll two six-sided dice and record the sum of the numbers on the top faces.

2. Calculating Probability of a Sum of 7:

What is the probability of rolling a sum of 7?

Step 1: List all possible outcomes when rolling two dice (there are 36 total outcomes).

Step 2: Identify the combinations that result in a sum of 7.

Step 3: Calculate the probability:

Fraction: Number of successful outcomes / Total outcomes

Decimal: Convert the fraction to a decimal.

Percentage: Convert the decimal to a percentage.

3. Predicting Other Sums:

Predict the probabilities for other possible sums (2 to 12). What sums do you think are more likely to occur? Why?

Questions to Answer:

1. After calculating the probability of rolling a sum of 7, what did you find?

Express your answer in fractions, decimals, and percentages.

2. What are the probabilities of rolling sums of 2, 3, 4, 5, 6, 8, 9, 10, 11, and 12?

How do these compare to the probability of rolling a sum of 7?

3. Which sum has the highest probability? Which has the lowest?

Explain why certain sums are more likely than others based on the outcomes.

4. If you roll the dice 60 times, how many times would you expect to roll a sum of 7 based on your probability calculation?

Extensions:

1. Experiment with More Rolls:

Roll the two dice multiple times (e.g., 30 rolls) and record the results. Compare your experimental results to your theoretical probabilities. Did they match? Why or why not?

2. Graphing Results:

Create a bar graph to represent the frequencies of each sum you rolled. How does this visual representation help you understand the probabilities?

3. Changing the Dice:

What if you used different types of dice (e.g., a 10-sided die or two 8-sided dice)? How would this affect the probabilities of the sums? Calculate the new probabilities.

4. Real-Life Applications:

Discuss a situation in real life where understanding probabilities (like rolling dice) is important. How can this knowledge help in decision-making?

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1. Flipping the Coin:

Flip a coin 50 times and record the results. Keep a tally of how many times you get heads and how many times you get tails.

2. Calculating Experimental Probability:

Determine the experimental probability of getting heads:

Step 1: Count the number of heads you flipped.

Step 2: Calculate the experimental probability using the formula:

Experimental Probability of Heads=Number of Heads/50

Express this probability as a fraction, decimal, and percentage.

3. Theoretical Probability:

The theoretical probability of getting heads in a fair coin flip is:

Theoretical Probability of Heads=12=0.5=50%\text{Theoretical Probability of Heads} = \frac{1}{2} = 0.5 = 50\%Theoretical Probability of Heads=21​=0.5=50%

Questions to Answer:

1. What was the experimental probability of getting heads based on your 50 flips?

Express this in fractions, decimals, and percentages.

2. Compare your experimental probability of heads to the theoretical probability.

How close were they? Were there any significant discrepancies?

3. If there was a discrepancy, what do you think might have caused it? Discuss factors that can affect experimental results in probability.

4. If you were to flip the coin 100 more times, do you think the experimental probability would get closer to the theoretical probability? Why or why not?

Extensions:

1. Repeated Trials:

Perform the coin flip experiment multiple times (e.g., 5 sets of 50 flips).

Compare the experimental probabilities from each trial. Do they vary widely or stay consistent?

2. Graphing Results:

Create a bar graph to display the number of heads versus tails for your 50 flips.

How does this visual representation help you understand the outcomes?

3. Analyzing Long-Term Trends:

Discuss the Law of Large Numbers. How does it relate to your results?

What might happen if you flipped the coin an extremely large number of times?

4. Real-Life Applications:

Consider a real-world situation where understanding experimental and theoretical probabilities is important (e.g., games of chance, insurance). How can this knowledge influence decision-making in that context?

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Scenario:

You have collected data on the average daily temperatures (in °C) and the amount of rainfall (in mm) for a week in Hong Kong.

Choose a way to represent the data:

1. Bar Graph:

Create a bar graph to represent the average daily temperatures for the week. Label the x-axis with the days of the week and the y-axis with the temperatures.

2. Histogram:

Create a histogram to represent the amount of rainfall for the week. Use appropriate intervals for the rainfall amounts.

3. Pie Chart:

Calculate the total rainfall for the week and represent the proportion of rainfall for each day in a pie chart. Label each section with the percentage of total rainfall.

4. Line Graph:

Create a line graph to show the changes in temperature throughout the week. Connect the points to illustrate trends.

Questions:

1. Interpret the Graphs:

What trends do you notice in the temperature over the week?

Which day had the highest temperature? Which day had the lowest?

How does the amount of rainfall relate to the temperature on the corresponding days?

2. Real-Life Application:

Based on your graphs, how might the weather patterns in Hong Kong affect outdoor activities during the week? Provide a few examples.

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Scenario:

During the annual school sports day, students participated in three events: the 100-meter dash, long jump, and relay race. Below are the results for the three events in terms of the time taken (in seconds) and distances jumped (in meters) by each participant.

Data: ( is displayed below)

Tasks:

1. Calculate the Average:

Find the average time for the 100-meter dash.

Find the average distance for the long jump.

Find the average time for the relay race.

2. Determine the Best Performer:

Identify the fastest runner in the 100-meter dash.

Identify the student with the longest jump in the long jump event.

Identify the fastest relay team.

3. Create a Bar Graph:

Create a bar graph to represent the average time for the 100-meter dash and the relay race.

Create a separate bar graph to show the average distance for the long jump.

4. Interpret Your Findings:

Discuss the results with your classmates:

Which event had the fastest average time?

How do the long jump distances compare among the students?

What trends do you notice from your graphs?