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

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Presentation transcript:

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

Intro to Binomial Distribution AS Maths with Liz Stats 1

Factorial Notation = 24 = 120

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

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

Combinations formula

You try… (a) (b)

Combinations in your calculator Example 3 – try it!

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

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

Example 2 – Binomial Distribution

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.

You try!

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