SOLUTION: 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 percentag

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

========================================================

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(52777) (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
~~~~~~~~~~~~~~~~

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.

RELATED QUESTIONS
A can contains 7 pink balls and 5 blue balls. FOUR balls are selected without... (answered by stanbon)
According to which view of probability are the probabilities of events based on observed... (answered by edjones)
A new process or constructing I-pods is said to produce defects in only 5% of units... (answered by ewatrrr)
i need help on this problem here it is: a door is painted pink and blue. the area painted (answered by josmiceli)
Find the number of ways of placing 15 pebbles in a row given that 2 are yellow, 4 are... (answered by swincher4391,ewatrrr)
. If 10% of all disk drives produced on an assembly line are defective, what is the... (answered by ewatrrr)
On an assembly line an average of 15 products are boxed every minute. In any randomly... (answered by ewatrrr)
squares, circles and pentagons in the ratio 3:4:1 respectively. The shapes are either... (answered by math_tutor2020)
Working with Events: Suppose your top drawer contains different colored socks: 10 are (answered by addingup)