Payment
-
Payment
Payment
Figure 6.6 Time Periods for Payment and Notice
Calculation of the probability that payment was made before notice was given
involved two preliminary steps:
(1)
For payment to occur before the notice, both payment and notice had
to be in the period of overlap, that is, 17.37 to 18.00. This was a period of 23
minutes. Reasoning for this proposition goes as follows. (i) The period for
payment begins at the start of the period of overlap. Before this time there can
be no payment so payment cannot be before
the notice. (ii) The period for
notice expires at the end of the period of overlap. After that time notice cannot
have been given, so in this case also payment cannot be made before the
notice. (iii) It follows that for payment to be before notice both notice and
payment must be in the 23 minute period between 18.37 and 18.00.
(2)
In half the cases where notice and payment occur in the 23 minute
period of overlap notice will be before payment; in the other half notice will be
after payment.
These steps lead to the following calculations to determine the probability of
payment being before notice:
Probabilities
Relevant probabilities are as follows:
Notice is given in the 23 minute period
23/30
Payment is made in the 23 minute period
23/60
Both notice and payment are in this period
(23/30) x (23/60)
Half these cases payment will be before notice
1/2
Calculation
Probability that payment is made before notice is given is one half the
probability that both notice and payment are in the 23 minute period. The
formula is:
(23/30) x (23/60) x (1/2)
=
529/3600
=
0.147 (approximately)
=
14.7% (approximately)
Conclusion
The probability that payment is given before notice is approximately 14.7%.
Comment
The reasoning in this case is open to criticism. In the case there was lack of
direct evidence. This is not the equivalent of all outcomes being equally likely
which is the precondition for classical probability.
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