Question 1198877: an assembly line produces plastic piggybanks that are either pink or blue. On average, 2.4% of the banks contain defects. Of the banks with no defects, 15% were blue. The percentage of all banks produced that are perfect pink piggybanks is
a) 82.6 b) 82.96 c) 85 d) 87.4 e) 95.2
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!
Answer: b) 82.96
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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 82.96% 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
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.
Answer by ikleyn(52776)  (Show Source):
You can put this solution on YOUR website! .
an assembly line produces plastic piggybanks that are either pink or blue.
On average, 2.4% of the banks contain defects.
Of the banks with no defects, 15% were blue.
The percentage of all banks produced that are perfect pink piggybanks is
a) 82.6 b) 82.96 c) 85 d) 87.4 e) 95.2
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Let x be the total number of all banks.
Then the number of all defective banks is 0.024x;
the number of banks with no defects is x-0.024x = 0.976x;
the number of the blue banks with no defects is 0.15*0.976x = 0.1464x;
the number of the perfect pink banks is 0.976x - 0.1464x = 0.8296x.
To get the percentage of the all banks produced that are perfect pink piggybanks,
divide 0.8296x by x and multiply by 100.
ANSWER. That percentage is 82.96.
Solved.
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