What is the probability that it will snow on Christmas day in Huntingdon?

1. What is the probability that it will snow on Christmas day in Huntingdon?

2. Lesson Objective Understand that some situations are too difficult to model using equally likely outcomes so probabilities need to be found using an alternative technique Understand how we can estimate the probability of an event using relative frequency

3. The Relative Frequency of an event Number of times the event occurs in the experiment = The total number of trials in the experiment Eg I check the weather every day in April. It rains on 8 of the days, what is the relative frequency of it raining in April? Eg Records suggest that the relative frequency of a bus being late in the morning is 0.1 Over a term of 34 days, on how many days would I expect the bus to be late?

5. MCPT Mathematics and Technology The Monty Hall Problem

6. About Let’s Make a Deal • Let’s Make a Deal was a game show hosted by Monty Hall and Carol Merril. It originally ran from 1963 to 1977 on network TV. • The highlight of the show was the “Big Deal,” where contestants would trade previous winnings for the chance to choose one of three doors and take whatever was behind it--maybe a car, maybe livestock. • Let’s Make a Deal inspired a probability problem that can confuse and anger the best mathematicians.

7. Suppose you’re a contestant on Let’s Make a Deal.

8. You are asked to choose one of three doors. The grand prize is behind one of the doors; The other doors hide silly consolation gifts which Monty called “zonks”.

9. You choose a door. Monty, who knows what’s behind each of the doors, reveals a zonk behind one of the other doors. He then gives you the option of switching doors or sticking with your original choice.

10. You choose a door. Monty, who knows what’s behind each of the doors, reveals a zonk behind one of the other doors. He then gives you the option of switching doors or sticking with your original choice. The question is: should you switch?

11. X X Win

12. X X Win

13. X Win X

14. Win X X

15. True or Not? At the start of the game there is a 1/3 chance of me picking the car. I now know one of the doors which has a zonk behind it, so there are two doors left, one of which has the car and one of which has a zonk. Therefore the chances of me winning the car is now 1/2 for either door. Conclusion: There is no point me changing my door Is this true?

16. We are going to simulate the game in pairs. One player in each pair will be Monty (the host) and the other player will be the contestant ‘The Changers’ will play the game and always change the door they select ‘The Stickers’ will play the game but never change the door they select. Each pair needs to play the game 10 times and record how many wins

18. The correct answer: You should change your choice, because the probability of you winning the car if you do is 2/3. You pick a door randomly Pick a door With a Zonk Pick a door With a Zonk Pick a door With a Car Keep Win a Zonk Change Win a Car Keep Win a Zonk Change Win a Car Keep Win a Car Change Win a Zonk

19. Plenary questions: Why do we need to use relative frequency? How do you calculate the relative frequency? Do you think you will get better results by calculating relative frequencies based on 10 experiments or 50 experiments?