Question

8. switched-conditionals fallacy. if it bleeds, it leads: nearly 60% of violent crime stories carried in the media show a green fanged alien being handcuffed and escorted into a police car. assume that (i) 57% of violent criminals are green-fanged aliens (so the media coverage is essentially unbiased); (ii) green-fanged aliens make up only 18.7% of the population; and (iii) 0.16% of the population are violent criminals. a green-fanged alien is seen on the way to the grocery store. what are the chances this alien is a violent criminal? 4

Answer 1

Using Bayes' theorem and given statistics, the chance that a green-fanged alien seen on the way to the grocery store is a violent criminal is approximately 0.4854%.

Step-by-step explanation:

To calculate the probability that a green-fanged alien is a violent criminal, we will use the given statistics:

• Green-fanged aliens make up 18.7% of the population.
• 0.16% of the population are violent criminals.
• 57% of violent criminals are green-fanged aliens.

Now, we apply Bayes' theorem. The probability that a person is a violent criminal given they are a green-fanged alien (P(V|A)) is:

P(V|A) = P(A|V) * P(V) / P(A)

where:

• P(A|V) = probability a violent criminal is an alien = 57%
• P(V) = probability of being a violent criminal = 0.16%
• P(A) = probability of being an alien = 18.7%

Substituting these values in, we get:

P(V|A) = 0.57 * 0.0016 / 0.187 = 0.004854

We multiply this by 100 to get a percentage, so there is about a 0.4854% chance a green-fanged alien seen on the way to the grocery store is a violent criminal.