Probability: Foreign vs Local in a City

[thedeath]

In a city where 30% occupants are foreign, the probability of a foreign being questioned is 40%, while for a local is 10%. What is the likelihood that any person chosen at random will be questioned.

 

[EnumaElish]

Look up the conditional probability formula:

http://en.wikipedia.org/wiki/Conditional_probability

 

[tacman]

The likelihood that any person chosen at random will be questioned in this city would be 22%. This can be calculated by taking the weighted average of the probability for a foreign being questioned (40%) and a local being questioned (10%), using the proportion of foreign and local occupants in the city (30% and 70%, respectively).

(40% x 30%) + (10% x 70%) = (0.4 x 0.3) + (0.1 x 0.7) = 0.12 + 0.07 = 0.19

Therefore, there is a 19% chance that a foreign person will be questioned and a 7% chance that a local person will be questioned. Adding these two probabilities together gives us a total of 26%. However, this includes the possibility that a person is both foreign and local, which is not possible. To adjust for this, we subtract the probability of a person being both foreign and local (30% x 10% = 3%) from the total, giving us a final likelihood of 26% - 3% = 22%.

In conclusion, in this city, there is a 22% likelihood that any person chosen at random will be questioned, taking into account the different probabilities for foreigners and locals being questioned and the proportion of foreign and local occupants in the city.