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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

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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?

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    $\begingroup$ 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. $\endgroup$ – John Stud Jan 15 at 2:17

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