# 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...

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.

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### 1 Answer

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.**