6: Binomial & Poisson Distribution Flashcards
What is the formula for the probability of a successful outcome?
P (A) = M / N
Probability of event ‘A = Number of successful outcomes / Number of total outcomes
What are mutually exclusive and non-mutually exclusive events?
Mutually exclusive: Outcomes cannot occur at the same time
Non mutually exclusive: Outcomes can occur at the same time
What type of connective do mutually exclusive and non mutually exclusive events apply to?
‘or’
What is the formula for mutually exclusive events using the ‘or’ connective?
P (A or B) = P(A) + P(B)
What is the formula for NON mutually exclusive events using the ‘or’ connective?
P (A or B) = P(A) + P(B) - P(A and B)
What are independent and dependent events?
Independent: The outcome of one event does not effect the probability of another occurring
Dependent: Occurrence of one event effects the probability of another occurring
What is the formula for an independent event using the ‘and’ connective?
P (A and B) = P(A) * P(B)
What is the formula for a dependent event using the ‘and’ connective?
P (A and B) = P(A) * P(B/A)
P(B/A) = probability of B given A has occured.
What is the probability of an event, A, not occurring?
P(not A) = 1 - P(A)
Give an example for each of the following:
1) Mutually exclusive event (or)
2) Non mutually exclusive event (or)
3) Independent event (and)
4) Dependent event (and)
1) Tossing a coin
2) Drawing 1 card based on colour & suite
3) Rolling 2 dice
4) Drawing cards without replacement
What is the formula for the binomial coefficient?
What does each letter stand for?
^nCr = n! / (n-r)!*r!
r = specified successes
n = number of independent identical trials
In binomial distributions, what is the formula for the probability of having exactly ‘r’ successes in a given number of trials?
P(r) = ^nCr * p^r * q^n-r
Where:
p = probability of success in a single trial
&
q = probability of failure in a single trial
What is the formula for ‘q’, the probability of failure in a single trial?
q = 1 - p
How would you calculate the probability of the following events in a sample of 6:
1) No successful events
2) 1 successful event
3) More than 4 successful events
4) At least 2 successful events (= 2 or more)
1) P(0)
2) P(1)
3) P(5) + P(6)
4) 1 - P(0) + P(1)
When should the binomial distribution be approximated by the Poisson probability distribution?
When n*p < 5
What is the formula for the Poisson probability distribution?
What is Lambda equal to?
P(r) = (Lambda^r * e^-Lambda) / r!
Lamda is equal to the mean value, usually n*p
What is the first thing you should do in a Poisson probability question?
Check that Lambda is less than 5
How is lambda calculated in questions where probability of events is given during a fixed interval of time?
Use a call centre as an example with 30 calls in one hour and intervals of 1 minute and 5 minutes respectively.
Lambda = average rate of events
30 calls/60 mins = 0.5 call/min
for 1 min interval Lambda = 1*0.5=0.5 call/min
for 5 min Lambda = 5*0.5=2.5 call/5 min
How would you calculate the probability of the following events:
1) Probability of having 2 or 3 calls in a minute
2) Probability of having at least one call in 5 minutes
1) P (2 or 3) = P(2) + P(3)
2) P(at least 1) = 1 - P(no calls)
Given two companies with varying accident figures over the same time period, how would you calculate the associated success rates and probabilities for each?
Calculate the success rate: P(A) = M/N for each company using their respective information and note them down as P(A) and P(B) (for example)
Use the same probability formula for each, based on Binomial or Poisson’s distribution, but remember to use the ‘n’ and ‘r’ values for each respective data set.
How would you calculate the probability of both Company X AND Company Y expecting no accidents?
Company X P(0) * Company Y P(0)
How would you calculate the probability of a shipment containing less than 2 broken lamps on arrival?
P(0) + P(1)
LESS THAN 2, meaning only 0 or 1
