What is Binomial Distribution?
e.g. Throw a dice 20 times
2. Consists of 2 mutually exclusive outcomes
e.g. head or tail, defective or not defective, success or failure
Probability of success is p, probability of failure is 1 – p (which can also be expressed as q)
3. Consists of constant probability for each observation
e.g., each coin has the same probability of being a head
4. Observations are independent
i.e. the outcome of one observation does not affect the outcome of the other
The number of combinations of selecting X objects out of n objects is hence the binomial formula represented by:
NcX * P ^x * (1-p) ^ (n-x)
Where
n is the number of trials
c is the “choose” function in your scientific calculator (commonly noted as nCr in scientific calculator)
X is the number of selection
P is the probability of success
(1-P) is the probability of failure
Imagine you throw a coin 10 times, the probability of getting 2 “heads” is:
10 C 2 * 0.5 ^ 2 * 0.5 ^ 8
since the probability of getting head is –> 50% (0.5)
Got it? Now, try on your own:
There are 1000 computers in a shipment. Past information revealed that the defective rate per shipment is 10%.
What is the probability that:
a) at least 2 computers are defective?
b) at most 95 computers are defective?
c) exactly 5 computers are not defective?