Question 1192485
<font color=black size=3>
P(A) = 0.4
P(A') = 1 - P(A) = 1 - 0.4 = 0.6


P(C | A) = 0.0055
P(C' | A) = 1 - P(C | A) = 1 - 0.0055 = 0.9945


P(C' | A') = 0.0105
P(C | A') = 1-P(C' | A') = 1-0.0105 = 0.9895


To summarize so far, we have:
P(A) = 0.4
P(A') = 0.6
P(C|A) = 0.0055
P(C|A') = 0.9895


Now use the Law of Total Probability to be able to say the following
P(C) = P(C and A) + P(C and A')
P(C) = P(C | A)*P(A) + P(C | A')*P(A')
P(C) = 0.0055*0.4 + 0.9895*0.6
P(C) = 0.5959


Next, apply Bayes Theorem
P(A | C) = P(C | A)*P(A)/P(C)
P(A | C) = 0.0055*0.4/0.5959
P(A | C) = <font color=red>0.0036918946132</font>
The result is approximate.
Round that value however you need to.


Here's one useful calculator to check your work.
<a href = "https://www.gigacalculator.com/calculators/bayes-theorem-calculator.php">https://www.gigacalculator.com/calculators/bayes-theorem-calculator.php</a>
Type in these values
P(A) = 0.4
P(C|A) = 0.0055
P(C|A') = 0.9895
Make sure to click the radio button labeled "Proportions e.g. 0.05" before hitting "calculate".
<img width="50%" src="https://i.imgur.com/A7JFjYZ.png">
</font>