Chapter 2 supplementary exercises

• Supplementary Exercise 2.1

  A light aircraft, operating in a remote Antarctic area, has two air speed indicators. One (T) is based on a pitot tube and the other (G) is based on GPS measurements. The probability that T will fail during a flight is 0.1. The probability that G will fail during a flight is 0.02. Answer the following questions with probabilities that are correct to three decimal places.
  1. Suppose the failure of T and the failure of G are independent events.
     1. What is the probability that both T and G fail during a flight?
     2. What is the probability that T or G fails during a flight?
     3. What is the probability the neither T nor G fails during a flight?
  2. Now suppose the probability that T fails during a flight given that G fails during a flight is 0.5.
     1. What is the probability that both T and G fail during a flight?
     2. What is the probability that T or G fails during a flight?
     3. What is the probability the neither T nor G fails during a flight?
     4. What is the probability that G fails during a flight given that T fails during a flight?

  Solution:

  1. 1.   0.1 × 0.2 = 0.002
     2.   0.1 + 0.02 - 0.002 = 0.118
     3.   1 - 0.118 = 0.882
  2. 1.   0.02 × 0.5 = 0.010
     2.   0.1 + 0.02 - 0.01 = 0.110
     3.   1 - 0.110 = 0.890
     4.   0.01/0.1 = 0.1
     
     




• Supplementary Exercise 2.2

  A process produces aluminium castings. Let A be the event that a casting has excess flash and B be the event that a casting has a high porosity. Twelve percent of castings have high porosity. The probability that a casting has excess flash given that it has high prosity is 0.1. The probability that a casting has high porosity given that it has excess flash is 0.2.
  1. What is the probability that a randomly selected casting has high porsity or excess flash?
  2. What is the probability that a randomly selected casting has neither high porosity nor excess flash?



• Supplementary Exercise 2.3

  A small injection molding company has three machines A, B and C. The proportions of out of specification items produced by machines A, B and C are 0.01, 0.02 and 0.05 respectively. Production is 70% from A, 20% from B, and 10% from C.
  1. What proportion of the total production is out of specification?
  2. An inspector finds an item that is out of specification. What is the probability that it was produced on machine C?

  Solution:

  
  
  1.   0.7 × 0.01 + 0.2 × 0.02 + 0.1 × 0.05 = 0.016
  2.   0.1 × 0.05/0.016 = 0.3125