Estimate how many of the 1000 ex-cons committed felonies since their release.
The criminal justice system wants to know about repeat offenders, so they gather 1000 ex-cons who were released two years ago and not arrested since then. They want to know how many ex-cons have committed felonies since their release. Of course, none of those present would want to answer such a question. So the authorities ask everyone in the room to secretly flip a coin. Then they ask people to raise their hands If they flipped a head OR committed a felony. 620 people raise their hands. Estimate how many of the 1000 ex-cons committed felonies since their release.
The total number of ex-cons is 1000. We know according to basic probability theory, 500 out of this 1000 would get head and other 500 would get tail.
When the authorities asked for ex-cons who got head or commited a felony, 620 raised their hands. The other 380 are ex-cons who got tail and didn't commit felony.
Now out of this 620 who raised hands, 500 got heads. That means 120 (620-500) had commited felony and they got tails (500 got head and raised hands and they may have committed felony also, but 120 raised hands just because they committed felony). That means 120 has got tails and had committed felony.
Also it means out of the ex-cons who committed felony 120 had got tail. Now interestingly, according to probability thoery this should be the half of the ex-cons who committed felony. Because there is no relation in committing a felony and getting head or tail due to the fact that fliipping a coin is a completely fair and random incident.
Therefore, 120 of ex-cons who committed felony is the half of the ex-cons who committed felony.
Therefore, the number of ex-cons who committed felony can be estimated as `120 xx 2` which is 240.
The answer is 240.