Question 1198877
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Answer: <font color=red>b) 82.96</font>


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Work Shown:


D = has defects
~D = does not have defects


B = blue
~B = not blue, aka pink


P(D) = probability of a defect
P(D) = 0.024
P(~D) = probability of not a defect
P(~D) = 1 - P(D) = 1 - 0.024 = 0.976


P(B given ~D) = probability of selecting blue, given no defects
P(B given ~D) = 0.15
P(B given ~D) = probability of selecting pink, given no defects
P(~B given ~D) = 1 - P(B given ~D)
P(~B given ~D) = 1 - 0.15
P(~B given ~D) = 0.85


P(~B and ~D) = P(~B given ~D)*P(~D)
P(~B and ~D) = 0.85*0.976
P(~B and ~D) = 0.8296


The probability of selecting a piggybank that is both pink and without defects is 0.8296
This converts to the <font color=red>82.96%</font> after moving the decimal point two spots to the right (same as multiplying by 100).


Here's a way to visually represent what's going on using a tree diagram
*[illustration Screenshot_163.png]
We don't have enough information to fill out the rest of the tree; luckily, we don't need that left side at all. We simply multiply the values along the highlighted path.
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