Computer keyboard failures are due to faulty electrical connects (12%) or mechanical defects (88%). mechanical defects are related to loose keys (27%) or improper assembly (73%). electrical connect defects are caused by defective wires (35%), improper connections (13%), or poorly welded wires (52%). a) find the probability that a failure is due to loose keys. b) find the probability that a failure is due to improperly connected or poorly welded wires.

Probability that a failure is due to loose keys = 0.2376

Probability that a failure is due to improperly connected or poorly welded wires  0.078

Step-by-step explanation:

Given data:

P(A) = percentage of faulty electrical connections is 12% = 0.12

P(B) = mechanical defects is 88% =  0.88

P(C / B ) = percentage of defects that are related to loose keys is 27% =  0.27

P( D/B ) = improper assembly is 73% = 0.73

P(E/A) =  defective wires  is 35% =  0.35

P( F/A)= improper connections is 13% =  0.13

P( G/A ) = percentage of poorly welded wire is 52% = 0.52

a) Probability of being failure because of loose keys = 0.27\times 0.88 = 0.2376

b) Improperly connected = 0.13\times 0.12 = 0.0156

    poorly welded wires= 0.52 \times 0.12 = 0.0624

Probability of being failure because of improperly connected or poorly welded wires = 0.0156 + 0.0624 = 0.078

a) 23.76%

b) 7.8%

Step-by-step explanation:

a) probability that a failure is due to loose keys.

loose key failure (27%) comes under mechanical failure(88%)

hence, probability that a failure is due to loose keys= 0.27×0.88= 0.2376= 23.76%

b)  probability that a failure is due to improperly connected wire which comes under electrical failure = 0.12×0.13

probability that a failure is due to poorly welded wires which comes under electrical failure= 0.52×0.12

now, the probability that a failure is due to improperly connected or poorly welded wires. = 0.12(0.52+0.13)= 0.078= 7.8%

452,489 to the nearest thousand is 452,000

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