# School Theft Quiz Puzzle Answer

There has been a theft at the school near to Quiz Master Shop Towers. Luckily there is an eyewitness who saw the thief escaping. The eyewitness has reported that the thief was in school uniform and wearing a blazer, as opposed to a jumper.

Police research has shown that in these cases an eyewitness is correct 80% of the time. It is also known that 85% of the pupils at the school wear jumpers and not blazers, which has increased the chances of finding the culprit.

What is the probability of the thief wearing a blazer?

Let us assume that there are 100 pupils at the school, 85 of whom wear jumpers and 15 wear blazers, and they all steal something once.

For the 85 jumper-wearing thieves, the eyewitness will report that they were wearing a jumper 68 times (80% of 85) and will report they were wearing a blazer 17 times (20% of 85).

Likewise, for the 15 blazer-wearing thieves, the eyewitness will report that they were wearing a jumper 3 times (20% of 15) and will report they were wearing a blazer 12 times (80% of 15).

From this we can see that the eyewitness will report a blazer wearer 29 times, and that on 12 of those occasions the thief will be wearing a blazer. So there is a 12/29 chance or 41% that the thief was wearing a blazer.