# Conditional Probability Problem Computation / Setup Check

I am looking for some help or validation of setup of a conditional probability problem. The details and the way I went about it are below!

# Conditional Probability

Givens:

• P(First) = guerillas attack villages at time $$t$$
• P(Second) = guerillas attack same villages at time $$t+1$$
• total_villages = 300

• 15 (0.05) of the villages were attacked at time $$t$$

• 21 (0.07) of the villages were attacked at time $$t+1$$

• 12 (0.04) were attacked in both periods

$$P(\text{Second|First}) = \frac{P(\text{First and Second})}{P(\text{First})}$$

= $$\frac{0.04}{0.05}$$ = 0.8

## 1 Answer

Yes, your working is fine. We just have to use the formula of conditional probability.

Notice that the information that the number of villages being attacked at time $$t+1$$ is not used as it is not required in the formula of the conditional probability.

Remark: I am slightly curious about the wording "Of those attacked at time $$t$$". Does removing it change the meaning of the question? If the original question given in probability or exact counts?

• Thank you for the review! I removed the wording "Of those attacked at time $t$" because you are right, it is poorly worded and does not belong. – John Stud Jan 15 at 2:17