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Asked: 2020-11-13T22:23:19+05:30 In:

Extensive analysis of failure reports on an automotive component shows that there is a 7 in 10 chance that the failure is caused by fatigue and a 4 in 10 chance that it is due to corrosion. The probability that the cause of failure is both fatigue and corrosion is 0.2. What is the probability of failure being due to fatigue or corrosion?

Extensive analysis of failure reports on an automotive component shows that there is a 7 in 10 chance that the failure is caused by fatigue and a 4 in 10 chance that it is due to corrosion. The probability that the cause of failure is both fatigue and corrosion is 0.2. What is the probability of failure being due to fatigue or corrosion?
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    1. Platinum GATE Metallurgy Coaching

      P(F) is 0.7, probability of failure due to fatigue P(C) is 0.4, probability of failure due to corrosion P(F∩C) = 0.2, probability of failure due to fatigue and corrosion P(F∪C)=?, probability of failure due to fatigue or corrosion So, P(F∪C) = P(F) + P(C) -P(F∩C) = 0.7+0.4-0.2 =0.9

      P(F) is 0.7, probability of failure due to fatigue

      P(C) is 0.4, probability of failure due to corrosion

      P(F∩C) = 0.2, probability of failure due to fatigue and corrosion

      P(F∪C)=?, probability of failure due to fatigue or corrosion

      So,
      P(F∪C) = P(F) + P(C) -P(F∩C)

      = 0.7+0.4-0.2

      =0.9

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