### Q$-3-4$ Bayes's Rule $(5$ pts$)$

In the eastern coastal region of the United States:

$-$ Dangerous fires are rare $(`1\mathrm{.}1\%`)$

$-$ But smoke is fairly common $(`12\%`)$ due to barbecues,

$-$ And $`95\%`$ of dangerous fires make smoke

$**$What is the likelihood of a fire occurring when smoke is observed?$**$