1. Welcome to… Charlie’s House of Chance A brand new reality T.V. show where contestants have the chance to win £1,000,000.

2. At the beginning of the show there are 12 contestants in the house. Each week, the contestants must nominate other contestants for eviction. The last contestant left in the house wins the big money prize. One of the nominated contestants is chosen at random by a computer and is then evicted from the house.

3. The nominations for the first week are in. The contestants up for eviction this week are: Brian 24 Scotland Teacher Bryony 22 Scotland Vet Brad 19 Northern Ireland Mechanic Bob 31 England Psychologist Brian 24 Scotland Teacher Bryony 22 Scotland Vet Brad 19 Northern Ireland Mechanic Bob 31 England Psychologist All the contestants up for eviction are nervous – anyone could be chosen at random by the computer. Can you help the contestants figure out their chances of survival in the house?

4. Remember, the chance of something happening is just how likely it is to happen. The probability of something happening is equivalent to the chance of it happening.

5. Calculate the probability that: 1 a. Brian will be evicted. d. Bob will be evicted. c. Brad will be evicted. b. Bryony will be evicted.

6. Calculate the probability that: 1 Solution There is only 1 Brian out of 4 possible people. So there is a 1 in 4 chance that the person evicted will be Brian. 1 in 4 can be written as. So the probability that Brian will be evicted is a. Brian will be evicted. 1414 1414

7. Calculate the probability that: 1 Solution Probability = No. of favourable outcomes No. of possible outcomes Probability = No. of Brians______ No. of people up for eviction Probability = 1 4 (Remember: you might have to simplify fractions!) a. Brian will be evicted.

8. Calculate the probability that: 1 a. Brian will be evicted. d. Bob will be evicted. c. Brad will be evicted. b. Bryony will be evicted. 1414 1414 1414 1414

9. Calculate the probability that the person evicted : 2 b. Will be female. d. Will be Scottish. a. Will be younger than 25. e. Will be younger than 23. f. Will be of an age that is an odd number. h. Will be Welsh. c. Has exactly 3 vowels in their job title. g. Has the letter ‘b’ in their name. i. Will be older then 17.

10. b. Will be female. d. Will be Scottish. a. Will be younger than 25. e. Will be younger than 23. 3434 3434 1414 1212 f. Will be of an age that is an odd number. h. Will be Welsh. c. Has exactly 3 vowels in their job title. g. Has the letter ‘b’ in their name. 1212 1 1212 0 i. Will be older then 17. 1 Calculate the probability that the person evicted : 2

11. A probability scale is a method of displaying how likely an event is to occur. ½ meaning that the event has an even chance of happening 1 meaning that the event is certain 0 meaning that the event is impossible The scale goes from 0 to 1 with a probability of 01 impossiblecertainunlikelylikelyeven

12. Think about the following events and how likely each is to occur. a)The Sun will rise tomorrow. b)Britney Spears will become Prime Minister. c)You will win the lottery. d)It will rain this afternoon. e)You’ll have your favourite food for dinner tonight. f)Roll a dice and get a 4. g)Brian will be evicted. Likely? Unlikely? Certain? Impossible?

13. 01 impossiblecertainunlikelylikelyeven Construct a probability scale showing the chance of each event occurring. Place each letter on the scale similar to the example below. pq r s t u vw (If more than one event has the same probability write it above the other as shown.)

14. 01 impossiblecertainunlikelylikelyeven Construct a probability scale showing the chance of each event occurring. Place each letter on the scale similar to the example below. a)The Sun will rise tomorrow. b)Britney Spears will become Prime Minister. c)You will win the lottery. d)It will rain this afternoon. e)You’ll have your favourite food for dinner tonight. f)Roll a dice and get a 4. g)Brian will be evicted.

15. Use your results for the questions you have already answered and place each letter on the scale similar to the example below. (If more than one event has the same probability write it above the other as shown.) Construct a probability scale showing the chance of the events in Question 2 (a – i) occurring. 01 impossiblecertainunlikelylikelyeven pq r s t u vw

16. A T.V. Chat Show Host asks who you think will be the first person evicted. Can you say for sure who will be evicted? Why not?

17. The chat show host won’t give up – he really wants an answer. You have to tell him something. 1)He/she will be Scottish 2)He will be male 3)He/she will be younger than 23 4)He will be called Bob The Chat Show Host asks why you say this. What do you tell him? What piece of information about the evictee do you think is most likely to be true?

18. There’s breaking news: The computer that selects the evictee has contracted a virus. It cannot now select anyone with the letter ‘o’ in their name. Does this change your prediction?

19. 120,000 people entered to become contestants on the show. (You might want to take a note of these statistics!) Only a lucky 12 were randomly selected by a computer to become contestants.

20. 3 c. How many contestants must be Scottish? The rules state that exactly 25% of the contestants must be Scottish. There are no other rules concerning the nationality of contestants. d. For each Scot who entered, calculate the probability of becoming a contestant. a. For each person who entered, calculate the probability of becoming a contestant. e. Assuming randomness, what is the probability that the winner will be Scottish? 40,000 Scottish people entered to become contestants. b. Assuming randomness, for each person who entered, calculate the probability of winning.

21. c. How many contestants must be Scottish? The rules state that exactly 25% of the contestants must be Scottish. There are no other rules concerning the nationality of contestants. d. For each Scot who entered, calculate the probability of becoming a contestant. a. For each person who entered, calculate the probability of becoming a contestant. 1 10, 000 e. Assuming randomness, what is the probability that the winner will be Scottish? 40,000 Scottish people entered to become contestants. b. Assuming randomness, for each person who entered, calculate the probability of winning. 1 120, 000 3 3 40, 000 1414 3

22. The annoying Chat Show host is back. Is he correct? He has heard rumours that Charlie’s House of chance is fixed. Why/why not? He says that a Scot had a better chance of becoming a contestant than someone who is not Scottish.

23. Is he correct? It turns out that the Chat Show Host entered to become a contestant on Charlie’s House of Chance. What assumptions do you have to make to answer that question? He believes that he’d have a better chance of winning the lottery than he ever had of winning Charlie’s House of Chance. (Hint: the chance of winning the lottery jackpot is 1 in 14,000,000)