A.) P(defective | foo) = P(defective & foo)/P(foo)
4% = P(defective & foo)/30% . . . . . . . . . plug in the given data
0.04*0.30 = P(defective & foo) = 0.012 = 1.2%
The probability that a widget was produced at the foo factory and is defective is 1.2%.
b.) P(defective | foo) ≠ P(defective) (4% ≠ 5%), so the events P(defective) and P(foo) are NOT independent.
c.) P(foo | defective) = P(defective & foo)/P(defective)
P(foo | defective) = 1.2%/5% = 24%
The probability that a widget was produced at the foo factory given it is defective is 24%.
To find the tan x use the following formula
tan x = (sin x)/(cos x)
tan x = (1/2)/(sqrt (3)/2)
tan x = 1/sqrt (3) = sqrt (3)/3 or E
