## Consider the following evidence:

Dan and Paul were business partners in a junkyard. Both had previously served time in prison for offences of violence associated with gang activities, but both had claimed to have gone straight. Dan is shown to be in financial difficulties due to gambling debts. Unexpectedly, Paul has disappeared. There is very little evidence about what could have happened to him, but as his business partner, Dan stands to benefit from their share of the partnership. The police suspect that Dan may have murdered Paul.

What probability would you personally assign to the view that Dan murdered Paul given this evidence? Note that there is no ‘right’ answer. It is completely up to your judgement. Enter a value between 0 (impossible) and 1 (certainty). You can also enter it as a percentage if you prefer, between 0% (impossible) and 100% (certainty) Your probability will automatically be converted into a likelihood ratio. Feel free to put in different values to see how the likelihood ratio changes.

Enter fraction:
or enter percentage: %
This probability equates to a likelihood ratio of ??

The police decide to bring in a cadaver dog to search the junkyard. No body is found, but the dog indicates that there was a cadaver in the junkyard at some point. An expert is asked to give a likelihood ratio for the possibility that a cadaver was actually in the junkyard. She calculates this using the values we worked out above as follows:

Likelihood ratio

- probability dog indicates if there was a cadaver/probability dog indicates if there was not a cadaver
- 0.95/0.03
- 32

The final likelihood ratio can be updated using Bayes' Rule to take into account the expert evidence by multiplying your likelihood ratio and the expert’s likelihood ratio together:

?? x 32 =??

This can be converted back to a probability = [y/1+y] = ??

According to Bayes' Rule, if your initial probability was x / x% to being with, then after the expert evidence, it should be updated to be y / y%.

As you can see, because the expert value remains the same and is not dependent on the values you give, the expert's opinion is admissible because they are not expressing a view on any of the other evidence.