 Genetic Fingerprinting was developed by Professor Alec Jeffreys at the University of Leicester in 1984.

The technique is based on the fact that each of us has a unique genetic make-up, contained in the molecule DNA, which is inherited from our natural parents, half from our mother and half from our father.

DNA can be extracted from cells and body fluids and analysed to produce a characteristic pattern of bands or genetic 'fingerprint'.

The sketch below shows how genetic fingerprinting can be used to identify a child's father.

Equally important has been the use of genetic fingerprinting in rape cases, where the semen of the attacker and alleged attacker can be compared.

It is usual to compare between 10 and 20 bands. Experimental evidence has shown that in unrelated people the probability of one band matching is one in four. (0.25)

So for example, the probability of two bands matching

= (0.25)2

= 0.0625 or a 1 in 16 chance.

Problem 1        Find the probability of 10 bands matching. Express your answer in the form "1 in ? chance"

Problem 2        Repeat Problem 1, but using 0.5 as the probability of any single band matching.

You will have noticed that the answer to Problems 1 and 2 change quite dramatically if the underlying probability changes. In fact, the value of 0.25 has been the subject of some speculation recently in a number of criminal trials.

Problem 3        Copy and complete the table below. Comment on the values found and suggest the number of bands which should be compared, to be confident of a match not happening be chance, when the probability is 0.25.

Probability

Number of bands

(p)

5

10

15

20

0.2

1 in 3125

?

?

1 in 9.5 million million

0.25

?

?

?

?

0.5

?

?

?

?

EXTENSION   If p=0.25 and we wish the probability of a complete match not happening by chance to be 1 in 50 million (approximately the population of Britain), how many bands need to be compared?