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Three probability questions

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1. A system contains two components, A and B. The system will function so long as either A or B functions. The probability that A functions is 0.95, the probability that B functions is 0.90, and the probability that both function is 0.88. What is the probability that the system functions?

2. A system contains two components, A and B. The system will function only if both components function. The probability that A functions is 0.98, the probability that B functions is 0.95, and the probability that either A or B functions is 0.99. What is the probability that the system functions?

3. Let V be the event that a computer contains a virus, and let W be the event that a computer contains a worm. Suppose P(V) = 0.15, P(W) = 0.05, and P(V ∪ W) = 0.17.
a. Find the probability that the computer contains both a virus and a worm.
b. Find the probability that the computer contains neither a virus nor a worm.
c. Find the probability that the computer contains a virus but not a worm.

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Solution Summary

Step-by-step explanations and calculations are given.

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1.
The following are given:
P(A) = 0.95,
P(B) = 0.90 and
P(A ∩ B) = 0.88
Find P(A ∪ B).

Use the addition rule.
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
= 0.95 + 0.90 - 0.88 = ...

Solution provided by:
J Pye, MSc
Education
  • MSc, California State Polytechnic University, Pomona
  • MBA, University of California, Riverside
  • BSc, California State Polytechnic University, Pomona
  • BSc, California State Polytechnic University, Pomona
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