Business Modelling
Business Modelling Revision
Mutually exclusive event- add the probabilities together to find the probability that one or other of the events will occur. E.g men/woman
P(A or B)= P(A)+P(B)
Non mutually exclusive- shared characteristic
P (A or B)= P(A) + P(B) – P(B+A)
Independent events – outcome is known to have no effect on another outcome
P (A+B) = P(A) X P(B)
Dependant events- outcome of one event affects the probability of the outcome of the other. Probability of the second event said to be dependent on the outcome of the first.
P (A+B) = P(A) P(B/A)
Bionomial distribution, used when a series of trails have the following characteristics:
Each trial has two possible outcomes
The two outcomes are mutually exclusive
There are constant probabilities of success, p and failure, q=1-p
P( r successes in n trials) =
Example using the binomial distribution
A company employs a large number of graduates each September . In spite of careful recruitment including interviews and assessment centres, the company finds that 2% of graduates have left the company within one month of starting. Use the binomial distribution to find the probability that:
i) Three out of a sample of 10 graduates will have left the company within one month of starting. – Binomial with n= 10, p=0.02. P(three leave) = 10c3, 0.02^3, (0.98)^97 =0.0008334 Three out of ten leaving is clearly very unlikely. ii) n=100 p=0.02 , 100c3, 0.02^3, (0.98)^97= 0.182
Poisson distribution- close relative of the bionomial distribution and can be used to approximate it when
The number of trials, n is large
The probability of success, p, is small
Also useful for solving problems where events occur at random
Main difference between the bionomial and poisson distributions is that the bionomial distribution uses the probabilities of both success and failure, while the poisson uses only the probability of successes.
P( r successes) =
Normal distribution
Both the bionomial and poisson distributions are used
Mutually exclusive event- add the probabilities together to find the probability that one or other of the events will occur. E.g men/woman
P(A or B)= P(A)+P(B)
Non mutually exclusive- shared characteristic
P (A or B)= P(A) + P(B) – P(B+A)
Independent events – outcome is known to have no effect on another outcome
P (A+B) = P(A) X P(B)
Dependant events- outcome of one event affects the probability of the outcome of the other. Probability of the second event said to be dependent on the outcome of the first.
P (A+B) = P(A) P(B/A)
Bionomial distribution, used when a series of trails have the following characteristics:
Each trial has two possible outcomes
The two outcomes are mutually exclusive
There are constant probabilities of success, p and failure, q=1-p
P( r successes in n trials) =
Example using the binomial distribution
A company employs a large number of graduates each September . In spite of careful recruitment including interviews and assessment centres, the company finds that 2% of graduates have left the company within one month of starting. Use the binomial distribution to find the probability that:
i) Three out of a sample of 10 graduates will have left the company within one month of starting. – Binomial with n= 10, p=0.02. P(three leave) = 10c3, 0.02^3, (0.98)^97 =0.0008334 Three out of ten leaving is clearly very unlikely. ii) n=100 p=0.02 , 100c3, 0.02^3, (0.98)^97= 0.182
Poisson distribution- close relative of the bionomial distribution and can be used to approximate it when
The number of trials, n is large
The probability of success, p, is small
Also useful for solving problems where events occur at random
Main difference between the bionomial and poisson distributions is that the bionomial distribution uses the probabilities of both success and failure, while the poisson uses only the probability of successes.
P( r successes) =
Normal distribution
Both the bionomial and poisson distributions are used