**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?