Binomial Distribution. The binomial distribution is used when there are exactly two mutually exclusive outcomes of a trial. These trials are often referred to as Bernoulli trials E.g. Flipping a Coin (Head or Tail) Rolling a Dice – HUH ??????
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The binomial distribution is used when there are exactly two mutually exclusive outcomes of a trial. These trials are often referred to as Bernoulli trials
Flipping a Coin (Head or Tail)
Rolling a Dice – HUH ??????
Well we could say the outcomes are getting a 6 and not getting a 6
These outcomes are appropriately labeled "success" and "failure". E.g. getting a 6 = success The binomial distribution is used to obtain the probability of observing x successes in N trials, with the probability of success on a single trial denoted by p.E.g. for each trial chance of a 6 =The binomial distribution assumes that p is fixed for all trials.
Tree diagrams can only go so far before they become cumbersome.
E.g. Rolling a Die in successive trials
3 rolls of a dice
Paths in Red show those outcomes which have two sixes
How many paths are there?
What is the probability at the end of each path?
There are 3 branches
Each branch has a probability of
WHY are they the same?
So the total chance of rolling two sixes in 3 trials is
Let p = rolling a 6 = 1/6 , q = not rolling a 6 =5/6
Let n = trials = 3
And let r = number of successes you desire
THE PREVIOUS CALCULATION
Would look like
No. arrangements of (ppq)
ppq = 3 arrangements from the tree diagram
What if you carried out 8 trials and wanted the probability of getting 2 sixes.
THAT IS A BIG TREE!
How many arrangements of ppqqqqq are there?
That’s right it is a combination!
And the good news
The Calculator has a function to do it all for you…Binompdf which is in the DISTR Menu
Just enter in (n, p, r)