Mathematics, 02.07.2019 01:30, ramirezzairap2u4lh

Three labs, a, b and c produce, respectively, 40%, 10% and 50% of our finished prescription glasses. the percentage of defective items produced by the labs is, respectively, 3%, 4% and 5%. a vip order is generated, randomly allocated to one of the three labs, and the finished pair of glasses are sent to headquarters. (a) find the probability that the pair of glasses are defective. (b) if the pair of glasses are defective, find the probability that it was produced by lab a lab b lab c

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answered: alove1777

Solution: Let's assume three labs produce 1000 pairs of glasses.

We know that 40% of glasses are produced by Lab A. Therefore, the number of pairs of glasses produced by Lab A is:

$40\% of 1000 = 0.4 \times 1000=400$

And number of defective glasses produced by Lab A is $0.03 \times 400=12$

Number of pairs of glasses produced by Lab B is:

$10\% of 1000=0.10 \times 1000=100$

And number of defective glasses produced by Lab B is $0.04 \times 100 =4$

Number of pairs of glasses produced by Lab C is:

$50\% of 1000=0.50 \times 1000=500$

And number of defective glasses produced by Lab C is $0.05 \times 500 =25$

(a)Find the probability that the pair of glasses are defective.

The probability that the pair of glasses are defective is:

$\frac{12+4+25}{1000}= \frac{41}{1000}=0.041$

(b)If the pair of glasses are defective, find the probability that it was produced by

lab A

lab B

lab C

The probability that it was produced by lab A is:

$\frac{12}{41}=0.2927$ rounded to 4 decimal places

The probability that it was produced by lab B is:

$\frac{4}{41}=0.0976
$ rounded to 4 decimal places

The probability that it was produced by lab C is:

$\frac{25}{41}=0.6098
$ rounded to 4 decimal places

answered: Guest

answer:

payment just for service

→

87.12

payment for service including tax

→

94.09

explanation:

service only with 20% tip

→

72.6

(

100

)

87.12

in the opening of the question the word 'service' is associated only with the pretax value.

the closing part of the question asks: how much did she pay for the

service

−−−−−−

so technically the answer is

→

72.6

(

100

)

87.12

however, the intention of the question provider may have been that your answer is to be

87.12

(

100

)

94.09

to 2 decimal places.

payment just for service

→

87.12

payment for service including tax

→

94.09

tony b

mar 21, 2017

answer:

trying to explain it another way

explanation:

service charge

→

72.60

20% tip

100

72.60

14.52

−−−−−−

←

add

87.12

tax

100

87.12

6.97

−−−−−

←

add

94.09

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Three labs, a, b and c produce, respectively, 40%, 10% and 50% of our finished prescription glasses....