An electronics shop has 4 computers, 2 of which are defective. When a diagnostic test is performed on a defective computer, there is a 90 % chance that the test will successfully confirm the computer is defective. However, when the same diagnostic is performed on a good computer, there is a 5 % chance that the test will wrongly report that the computer is defective. Two computers are chosen at random from the 4 available and the diagnostic test is performed independently on both. Find the probability that the test will report that both computers are defective.
Please provide full explanation step by step.
Answers
16.54 % Probability that both computers are defective.
Step-by-step explanation:
4 computers, 2 of which are defective.
Two computers are chosen at random from the 4 available
2 Computers can be selected in ⁴C₂ = 6 Ways
Computer Selected
1 - way : Both Defectives (²C₂) , Probability = 1/6
4 - ways : 1 Defective 1 ok(²C₁ * ²C₁)) , Probability = 4/6 = 2/3
1 - Way : Both OK (²C₂) Probability = 1/6
Showing both defectives in each case
(0.9)(0.9) = 0.81
(0.9)(0.05) = 0.045
(0.05)(0.05) = 0.0025
probability that the test will report that both computers are defective.
= (1/6)0.81 + (2/3)(0.045) + (1/6)(0.0025)
= (1/6)(0.81 + 0.18 + 0.0025)
= (1/6)( 0.9925)
= 0.1654
16.54 % Probability that both computers are defective.
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