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  • Consider a company that assembles computers. The probability of a faulty assembly of any computer is p. The company therefore subjects each computer to a testing process. This testing process gives

Consider a company that assembles computers. The probability of a faulty assembly of any computer is p. The company therefore subjects each computer to a testing process. This testing process gives the correct result for any computer with a probability of q. What is the probability of a computer being declared faulty?

Option: 1

\mathrm{p q+(1-p)(1-q)}


Option: 2

\mathrm{(1-q) p}


Option: 3

\mathrm{(1-p) q}


Option: 4

\mathrm{pq}


Answers (1)

best_answer

\text{Let A}= \left \{ \text{Computer declared faculty} \right \}, \mathrm{E_{1}}\left \{ \text{faculty computer} \right \}, \mathrm{E_{2}}=\left \{ \text{Non faculty computer} \right \}

\text{So P(A)}= \mathrm{P(E_{1})}.\mathrm{P(\frac{A}{E_{1}})}+\mathrm{P(E_{2})}.\mathrm{P(\frac{A}{E_{2}})} \left \{ \text{Using law of total prob.} \right \}

                                                            \mathrm{=p . q+(1-p)(1-q)}

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rishi.raj

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