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  • 1. Grade 7 | Unit 7.4 | Page 10 Unit 7.4 Learning Activity Sheet Chance and probability – coins and dice Fill in the names of your group members: ____________________________________________________________________________________________________ You may ask, “What is the probability of my correctly predicting the outcome, and thus of winning?” In your group, do the following exercises to find out the probability of winning or losing. Heads or tails? (Coins have a “head” side – the side with the South African emblem or coat of arms – and a “tail” side – the side with the amount written on it and the picture of a flower or animal.) 1. Use one coin for the following exercise. Toss a coin in the air. Write down the result on the line below. Now, toss it 5 more times and after each toss, write down the result. (H = “heads”; T = “tails”) _________ __________ ___________ ___________ __________ __________ 2. Before tossing the coin again, each person in the group must guess beforehand whether a “head” or “tail” will come up in the next three throws. Write your own three guesses in the three lines below (H = “heads”; T = “tails”): Your guesses _______ _______ _______ Now, once you’ve written down your predictions, a person in the group must toss the coin. Write down the actual side that comes up in the three throws. Actual result _______ _______ _______ 3. Look at the previous results above. Now, once again, guess the results of the next three tosses. Write down your own guess on the lines below: Your guesses _______ _______ _______ Now, once you’ve written down your predictions, a person in the group must toss the coin. Write down the actual side that comes up in the three throws. Actual result _______ _______ _______ 4. How many people in your group guessed correctly for both rounds? 5. There are 2 sides to a coin, therefore there are only two possible outcomes: heads or tails: Heads Tails Play a game in which you can bet only one outcome (Heads or Tails). Write down which outcome you wish to bet on: Your chances of winning are therefore: _________________ (Hint: divide your 1 predicted outcome by the number of possible outcomes.) 6. Note why you think coin tossing is a game of skill (the more skilful player is better able to determine the outcome) or a game of chance (it’s all just luck)?
  • 2. Grade 7 | Unit 7.4 | Page 11 Dice throwing As a group, complete the following: 1. Use one die (one die, two dice) for the following exercise. Before rolling the die, each person in the group must guess beforehand what three numbers will come up in the next three throws. Write your own three guesses in the three lines below (any number from 1 to 6): Your guess _______ _______ _______ Now, once you’ve written down your predictions, a person in the group must throw the die. Write down the actual number that comes up in the three throws. Actual result _______ _______ _______ How many of your guesses were correct? _________________________ 2. Now repeat the game but this time, instead of one die, use two dice. Before rolling the dice, guess the sum of the numbers that you think will come up in the next three throws. Write your three guesses in the three lines below (This will be any number from 2 to 12). Your guess _______ _______ _______ Once you’ve written down your predictions, a person in the group must throw the dice. Write down the actual sum of numbers that comes up in the three throws. Actual result _______ _______ _______ How many of your guesses were correct? ______________ 3. In dice throwing, using one die, there are 6 possible outcomes. What are they? But you can choose only one option. Your chances of correctly guessing the number are therefore: 1 chance in _______ (Hint: you can choose only 1 number, but there are 6 numbers on a die, therefore 6 possible choices.) 4. Here are all the possible ways in which a pair of dice can fall: Die 1 Die 2 How many possible ways can the dice fall in total: ___________ (Or put differently, how many possible outcomes are there in total?) 1:1 1:2 1:3 1:4 1:5 1:6 2:1 2:2 2:3 2:4 2:5 2:6 3:1 3:2 3:3 3:4 3:5 3:6 4:1 4:2 4:3 4:4 4:5 4:6 5:1 5:2 5:3 5:4 5:5 5:6 6:1 6:2 6:3 6:4 6:5 6:6
  • 3. Grade 7 | Unit 7.4 | Page 12 5. Write down all the possible ways (combination of two numbers) in which you can roll a sum of 7, using a pair of dice: _______ _______ _______ _______ _______ _______ (Hint: look at the table above and count all the various ways in which two numbers can add up to 7.) 6. What is the probability of your throwing a sum of 7 from two dice? _______________ (Hint: Divide the total number of possible ways the numbers from two dice can fall so that they add up to 7 by the total possible number of ways that the two dice can fall to give any sum at all.) 7. Write down all the possible ways (combination of two numbers) in which you can roll a total of 10, using a pair of dice: _______ _______ _______ (Hint: look at the table above and count all the various ways in which two numbers can add up to 10. There are 3 different ways of throwing a sum of 10.) 8. What is the probability of your throwing a total of 10 from two dice? _______________ (Hint: Divide the total number of possible ways the numbers from two dice can fall so that they add up to 10 by the total possible number of ways that the two dice can fall to give any sum at all.) 9. Let’s imagine that you bet on a “10”. Now roll the dice. Write down the actual outcome (the sum of the two dice): 10. Let’s continue to imagine that you bet again on a “10”. But, now blow hard on the dice before throwing them again. Write down the actual outcome: 11. You bet again on a “10”. But now, roll the dice softly when you throw them. Write down the actual outcome: 12. Now, based on the previous two outcomes, make a prediction about what the next sum will be when you roll the dice. Your prediction: Actual outcome: 13. Write down all the possible combinations in which you can roll a sum of 12, using a pair of dice: _____________ 14. What is the probability of your throwing a 12 with two dice? _______ 15. You bet on a “12”. Now roll the dice. Write down the actual outcome (the sum of the two dice): 16. You bet again on a “12”. But, before you roll the dice, concentrate hard on a 12, visualize the number 12 – now roll the dice. Write down the actual outcome: 17. You bet again on a “12”. But now, let the person who is feeling lucky throw the dice. Write down the actual outcome:
  • 4. Grade 7 | Unit 7.4 | Page 13 18. Now, try 5 more times to get a “12”. Actual outcome 1: Actual outcome 2: Actual outcome 3: Actual outcome 4: Actual outcome 5: 19. Do you think you can control the outcome of a game of dice? _________________ Can you predict with certainty what the outcome will be? ___________________ Are there some numbers that have a higher probability of appearing (i.e. a higher number of different ways in which the number can fall) than others? ____________ Is dice throwing a game of chance or a game of skill ? Why?___________________________________________________________________________________ THERE IS NOTHING YOU CAN DO OR THINK OR BELIEVE THAT WILL BRING ABOUT YOUR DESIRED RESULT. DICE IS A GAME OF PURE CHANCE!! AS ARE SLOT MACHINES AND COIN TOSSING.