The probability that a ship collision accident at sea which is attributed to nav

Question

The probability that a ship collision accident at sea which is attributed to navigational equipment (GPS) failure is diagnosed correctly is 0.75, and the probability that an accident which is not due to GPS failure is diagnosed incorrectly as being due to GPS failure is 0.30. If 35% of all accidents are due to GPS failures, find the probability that an accident is due to GPS failure, given that it has been diagnosed as being due to GPS failure. Substantiate your numerical answers with the appropriate Veitch diagram and associated probability calculations.

Hint: You’ll need to use all three (3) given pieces of data to come up with the final numerical answer.

Explanation / Answer

Solution:

Given,

P( GPS failure is diagnosed correctly) = P(A)= 0.75

P( GPS failure is diagnosed incorrectly) = P(B) = 0.30

P(GPS failure) =P(C) = 0.35

We have to find P( Accident due to GPS failure | GPS failure)….?

Formula = ( Accident due to GPS failure | GPS failure) = P(A) * P(B) / P(C)

              = (0.75*0.30) / 0.35

             = 0.6429

Done

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.