1. The information has been taken off these graphs. Can you think of a caption for each probability distribution? ab c

2. Today: Understand what a Probability Distribution is Learn about Binomial experiments Calculate probabilities

3. Example:

4. Number of heads, X 0 1 2 3 4 5 6 7 8 Frequency 12 9 6 3 0

5. Number of heads, X 0 1 2 3 4 5 6 7 8 Probability 0.4 0.3 0.2 0.1 0 Not very likely, but still possible!

6. A coin is flipped 8 times. X is the number of heads. a). Show that P(X = 0) is 1/256 b). Explain why P(X = 8) is the same as P(X = 0) c). Show that P(X = 1) = 0.03 d). Why is it harder to calculate P(X = 2)?

7. Are you psychic? Copy these 5 images onto paper. Concentrate on an image, does your neighbour know which image you are thinking of? Repeat this experiment 20 times and record how many you correctly get. a). Explain why the probability of success is 0.2 b). How many would you expect to correctly guess? c). Work out the probability of your score d). Calculate P(X = 18) e). Are there any assumptions we are making in this experiment? f).* Calculate P(X < 3)

8. This formula can be used to calculate probabilities: P(X = r) = n C r x p r x (1-p) n-r Example: A dice is rolled 5 times. Show the probability of getting exactly 3 sixes is around 3%

9. Practising the formula P(X = r) = n C r x p r x (1-p) n-r a). b). c).

10. Something different for a few minutes You have a choice of 10 cards, 1 2345678910 a). P(a multiple of 4) b). P(a prime number) c). P( n < 8) d). P(2 < n < 9) e). P(n < 7) f). P( n < 6)

11. The chance of Charlotte being late for school is 0.3 If X is the number of days late she is in a week, calculate the following: 1). Why is this an example of Binomial Probability? 2). What is the value of n and p? 3). P(X = 3) 4)*. P(X < 2) 5)**. P(X < 4)

12. Cumulative Binomial Distribution - The value is for P(X < x)

13. Using your formula book, a few to practise: 1). If n = 8, p = 0.4 P( X < 6) ? 2). If n = 14, p = 0.08 P( X < 2) ? 3). If n = 10, p = 0.5 P( X < 5) ? 4)*. If n = 25, p = 0.45 P( X > 13) ? 5)*. If n = 7, p = 0.09 P ( X > 4) ? 6)**. If n = 12, p = 0.4 P( 3 < X < 7) ?

14. Some practice of the Binomial Distribution: n = number of trials p = probability of success 1. n = 6, p = 0.2. Use the formula to calculate P(X = 3) 2. n = 9, p = 0.45. Calculate P(X = 7) 3.A quicker way of writing the distribution is X B(n, p) If X B(12, 0.7). Calculate P(X = 5) 4. X B(10, 0.3) Using the tables in the formula book, find a). P(X < 4) b). P(X < 7) c). P(X < 9) d). P(X > 6) 5. X B(12, 0.6) Using the tables, find a). P(X < 7) b). P(X > 6) c). P(3 < X < 8) 6. In a certain school, 30% of the students are members of the sixth form. a). Ten students are chosen at random. What is the probability that fewer than 4 of them are in the sixth form? b). If the ten students were chosen by picking ten who were sitting together at lunch, explain why a binomial distribution might no longer have been suitable.

16. Today Continuing our work on The Binomial Distribution Write down 3 things you can remember from last Tuesday’s lesson

17. It is estimated around 10% of the country’s population is vegetarian or vegan. In our class, (n = 20) X is the number of vegetarians or vegans. a). Give 2 reasons why the Binomial Distribution would be suitable here. b). P(X = 2) c). The probability of at most 4 vegetarians or vegans d). P(X > 5) e). How many vegetarians or vegans would you expect there to be in our class? f). If we asked in a girls only college, why might our results be different?

18. Why is this harder to answer?

21. 8 minutes

23. 10 minutes

26. Calculating the mean and standard deviation of binomial distributions. How many heads thrown?How many 6s rolled?

30. Last 25 minutes.... Either more Binomial Distribution on Page 86 of your textbook Or Revision of our Data and Probability work for a test next Tuesday!

32. Practise The Binomial Distribution at home – Page 86 - 87