Question

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.

Answer 1

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

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

Answer 2

a) 23.76%

b) 7.8%

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%