1. Starter - Combinations Once the first digit has been decided upon, how many options are there left for the second digit?

2. Intro to Binomial Distribution AS Maths with Liz Stats 1

3. Factorial Notation = 24 = 120

4. Factorials in your calculator When having to calculate larger factorials such as 12!, instead of calculating 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1… Here are the buttons to press in your CASIO FX-9750GII…  press MENU  select RUN MAT  type the number 12 (Let’s work out 12!)  press OPTN  press F6 to select the right arrow  press F3 to select PROB  press F1 to select x !  press EXE to get the answer

5. Example 1 - Combinations Solution: Write out all the possible combinations and eliminate the overlaps (in this case).

6. Combinations formula

7. You try… (a) (b)

8. Combinations in your calculator Example 3 – try it!

9. Characteristics of a binomial distribution  there are a fixed number of trials, n  there are only two possible outcomes: success or failure  let’s call the chance of success p  so the chance of failure is 1 – p  the trials are independent  the probability of success is fixed

10. Notation of Binomial Distribution this symbol means “has distribution” B means “binomial”

11. Example 2 – Binomial Distribution

12. You try! In a large population of animals, it is known that the proportion of males is 45%. A random sample of 10 animals is selected. Calculate the probability that the sample contains exactly 3 males.

13. You try!

14. Independent Study  Stats 1 Textbook:  pg. 70, Ex. 3A  pg. 72, Ex. 3B Optional Practise:  mymaths – combinations introduction  mymaths – the binomial distribution