The Experiment is repeated for a fix number of trials
The trials must be independant
There are only two pissible outcomes of interest for each trial. The outcomes can be classified as success (S) or as Failure (F)
The Probability of success P(S) is the same for each trial
Forumula:
P(X=X) = n! / (n-x)!x! * pxqn-x
Variables
P(X-x) or P(X) - Probability of success
n - Number of trials
p=P(s) - Number of successes
q=P(f) - Number of failures
x - Number of successes we are looking for.
A card is randomly selected from a deck and replaced. It is drawn 5 times, find the probability of drawing exactly 3 clubs.(52 cards in a deck, irrelevant. 4 suits, relevant)notice how easy it is to be thrown off
n=5 p=.25 q=.75 x=3
results
Another Example
Estimate the indicated Probability by using normal distribution as an approximation to Binomial distribution
A product is manufactued in batches of 240 and the overal rate of defects is 3%. First, Identify the variables: n, p, and q
n=240
p=.03
q=.97
Find the mean and Standard deviation of defects for each batch(for Binomial distributions we use these formulas: u=np o=√(npq))
u=240(.03)= 7.2. u=7.2
o = √n(.03)(.97)= 2.64. o=2.64
Find the probability that a randomly selected batch contains no more than 9 defects
we find z score then use algebra to find the answer 9-7.2/264= Z score