Question

Armed Questions

Assume there are 5,000 people surveyed. Of these, 20 actually used a gun defensively. Furthermore, assume that 5% of people lie when surveyed.

1. How many people who actually used a gun defensively will tell the surveyor that they did not use a gun defensively? How many will acknowledge their defensive gun use to the surveyor?

2. How many people who did NOT actually use a gun defensively will tell the surveyor that they did use a gun defensively? That is, how many false claims of defensive gun use will be made?

3. Use your answers above to determine how many claims of defensive gun use will be reported to the surveyor? What percent of these claims are true?

Answer 1

1) It is given that 20 out of 5000 people used gun defensively.

It is also given that 5% people lied when surveyed.

So, number of people who actually used a gun defensively, will tell the surveyor that they did use a gun defensively = 20 - (( 5/100 )*20)= 20-1 = 19.

Hence, 19 people will acknowledge their defensive gun usage.

2) Number of people who did not actually usable defensively but will tell the surveyor that they did use a gun defensively = The people who did not use the gun defensively and will lie to the surveyor

= (5000-20)*5/100

= 249 people.

3) So total number of claims of defensive gun use reported to the surveyor =

= 249+19

= 268 people.

The percentage of claims that are true = (19/268)*100 = 7.09%.

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