Probability – Experimental & Expectation – Activity A

Probability – Experimental & Expectation – Activity A This activity is designed to allow students to explore experimental & expected probabilities by constructing biased ‘casino games’. ‘Pre-Made’ games and ‘To Make’ games are included. Students could create their own from scratch. Other than unequal possible outcomes, students could weight the dice/spinners. The activity has flexible outcomes, but students should be able to discuss and write about their game and other students’.

Printing To print handouts from slides - Select the slide from the left. Then click: File > Print > ‘Print Current Slide’ To print multiple slides - Click on a section title to highlight all those slides, or press ‘Ctrl’ at the same time as selecting slides to highlight more than one. Then click: File > Print > ‘Print Selection’ To print double-sided handouts - Highlight both slides before using ‘Print Selection’. Choose ‘Print on Both Sides’ and ‘Flip on Short Edge’.

Disclaimer! A good mathematician would never gamble. There is no skill involved and you are playing by someone else’s rules. The odds are against you and you are guaranteed to lose money over time! Gambling can lead to addiction and people lose lots of money, and even relationships, because of gambling.

John and Julie have £10 each at the start of a game. John flips a coin and if it lands on tails he wins and gets £1 from Julie. If it lands on heads he loses and gives £1 to Julie. After 50 throws how much will John have? We expect John to win 50% of the time. During the game we expect John to win the same amount of money that he loses. P(Heads) = P(Tails) =

In Roulette people bet on a ball landing on a number or a colour. There are 38 numbers including 0 and 00.

If you bet on Red, and the ball lands on Red, you double your money. Jim starts with £5. He has the idea to always put £1 on Red. His money stays around £5. But over time he will lose all his money. Why?

P (RED) = P (BLACK) = P (GREEN) = Jim’s money would stay the same if There was only red and black. But if he plays 38 times, two times the ball will land on green. The probability of winning isn’t 50%. The odds are against him!

P (RED) = P (BLACK) = It’s biased! P (GREEN) = This is how casino’s take your money. Sometimes you win but more times you lose. Over time, you are guaranteed to lose all your money!

In roulette you will lose 53% of the time. The expectation is that if you play 100 times, you lose 53 times. The game looks fair, but in the long run you are guaranteed to lose! In this activity you will design a game for someone else to play. Your job is to design the game so it looks fair but the player would lose all their money eventually!

You can choose to make… Dicey Dice! In this activity you will design a game for someone else to play. Your job is to design the game so it looks fair but the player would lose all their money eventually! Lucky Landing! …or something you invent yourself! Super Spinner!

INSTRUCTIONS 1) Choose a game to make. 2) Decide how many WIN/LOSE outcomes you will have for your game. How else could you make your game biased? 3) Find someone to play the game 20, 25 or 50 times. Record how many wins/loses they get. Express the wins as a fraction and convert this to a percentage. Remember roulette was a 53% lose percentage. How close were you? Questions to Answer: Does your game look fair? Is it fair? Why? Why not? If someone played the game 100 times, how much money would they win/lose? Would you want to play your game? Next time, how would you change your game? Can you make it look even fairer?

Find someone to interview about their game. Do you like their game? Would you play it? Record their answers to the questions. You should be able to report back to the teacher about the student you interviewed and their game. Questions to Answer: Does your game look fair? Is it fair? Why? Why not? If someone played the game 100 times, how much money would they win/lose? Would you want to play your game? Next time, how would you change your game? Can you make it look even fairer?

There are 50WIN! squares and 50LOSE squares, so this game is notbiased. Is the distribution of the squares fair? If the dice/coin hits any side it must be re-thrown, is this fair?

FOLD & STICK Dicey Dice! LOSE LOSE In this game, the player makes a bet and rolls a tetrahedral dice (an equilateral pyramid). If the dice lands on WIN! the player gets double their bet. If the dice lands on LOSE they lose their bet. FOLD & STICK WIN! Construct the game and let someone play it 20, 25 or 50 times and record the results. LOSE Is this game fair? Why? Why not? Can you calculate the % probability of winning or losing? If the player plays 100 times, how many times would they win? If the player bet £1 each time, how much would they win/lose? FOLD & STICK INSTRUCTIONS Attach to cardboard and cut out the shape including the tabs. Fold & stick the tabs to make the tetrahedral dice.

Super Spinner! INSTRUCTIONS Attach to cardboard, cut out and carefully push a pencil through the centre hole. LOSE In this game, the player makes a bet and spins the octagonal spinner. If the spinner lands on WIN! the player gets double their bet. If the spinner lands on LOSE they lose their bet. WIN! WIN! WIN! LOSE LOSE LOSE LOSE WIN! WIN! Construct the game and let someone play it 20, 25 or 50 times and record the results. WIN! WIN! LOSE LOSE WIN! Is this game fair? Why? Why not? Can you calculate the % probability of winning or losing? If the player plays 100 times, how many times would they win? If the player bet £1 each time, how much would they win/lose? LOSE LOSE WIN!

Lucky Landing! FOLD & STICK FOLD & STICK FOLD UP In this game, the player makes a bet and throws a coin or dice into the tray. The ‘casino employee’ decides whether the dice is on a WIN! or a LOSE square. If the dice lands on WIN! the player gets double their bet. If the dice lands on LOSE they lose their bet. If the coin/dice hits any side then the player must re-throw! FOLD UP FOLD UP Construct the game and let someone play it 20, 25 or 50 times and record the results. Is this game fair? Why? Why not? Can you calculate the % probability of winning or losing? If the player plays 100 times, how many times would they win? If the player bet £1 each time, how much would they win/lose? FOLD & STICK FOLD & STICK FOLD UP

Dicey Dice! FOLD & STICK In this game, the player makes a bet and rolls a tetrahedral dice (an equilateral pyramid). If the dice lands on WIN the player gets double their bet. If the dice lands on LOSE they lose their bet. FOLD & STICK Decide how many WIN and LOSE outcomes your dice will have. How else could you make the game unfair? Complete the faces before constructing the dice. Let someone play the game 20, 25 or 50 times and record the results. FOLD & STICK Is your game fair? Why? Why not? Can you calculate the % probability of winning or losing? If the player plays 100 times, how many times would they win? If the player bet £1 each time, how much would they win/lose? INSTRUCTIONS Attach to cardboard and cut out the shape including the tabs. Fold & stick the tabs to make the tetrahedral dice.

Dicey Dice! In this game, the player makes a bet and rolls the 10-sided dice. If the dice shows WIN the player gets double their bet. If the dice lands on LOSE they lose their bet. VERY TRICKY! FOLD & STICK Decide how many WIN and LOSE outcomes your dice will have. How else could you make the game unfair? Complete the faces before constructing the dice. Let someone play the game 20, 25 or 50 times and record the results. FOLD & STICK Is your game fair? Why? Why not? Can you calculate the % probability of winning or losing? If the player plays 100 times, how many times would they win? If the player bet £1 each time, how much would they win/lose? INSTRUCTIONS Attach to cardboard and cut out the shape including the tabs. Fold & stick the tabs to make the dice.

Super Spinner! INSTRUCTIONS Attach to cardboard, cut out and carefully push a pencil through the centre hole. In this game, the player makes a bet and spins the spinner. If the spinner lands on WIN the player gets double their bet. If the spinner lands on LOSE they lose their bet. Decide how many WIN and LOSE outcomes your spinner will have. How else could you make the game unfair? Complete the spinner before constructing it. Let someone play the game 20, 25 or 50 times and record the results. Is your game fair? Why? Why not? Can you calculate the % probability of winning or losing? If the player plays 100 times, how many times would they win? If the player bet £1 each time, how much would they win/lose?

Lucky Landing! FOLD & STICK FOLD & STICK FOLD UP In this game, the player makes a bet and throws a coin or dice into the tray. The ‘casino employee’ decides whether the dice is on a WIN! or a LOSE square. If the dice lands on WIN the player gets double their bet. If the dice lands on LOSE they lose their bet. If the coin/dice hits any side then the player must re-throw! Decide how many WIN and LOSE outcomes your game will have. Complete the board before constructing it. Let someone play the game 20, 25 or 50 times and record the results. FOLD UP FOLD UP Is your game fair? Why? Why not? Can you calculate the % probability of winning or losing? If the player plays 100 times, how many times would they win? If the player bet £1 each time, how much would they win/lose? FOLD & STICK FOLD & STICK FOLD UP

Questions? Comments? Suggestions? …or have you found a mistake!? Any feedback would be appreciated . Please feel free to email: tom@goteachmaths.co.uk

Probability – Experimental & Expectation – Activity A