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4. Bayes Theorem - One way of thinking about Bayes theorem is that it converts a-priori...

4. Bayes Theorem - One way of thinking about Bayes theorem is that it converts a-priori probability to a-posteriori probability meaning that the probability of an event gets changed based upon actual observation or upon experimental data. Suppose you know that there are two plants that produce helicopter doors: Plant 1 produces 1000 helicopter doors per day and Plant 2 produces 4000 helicopter doors per day. The overall percentage of defective helicopter doors is 0.01%, and of all defective helicopter doors, it is observed that 50% come from Plant 1 and 50% come from Plant 2. [8 points]

(i) The a-priori probability of defective helicopter doors produced by Plant 1 is:

a. 0.0001

b. 0.5

c. 0.002

d. 0.0001 * 0.5

(ii) Probability of helicopter doors produced by Plant 1:

a. 0.5

b. 0.002

c. 0.4

d. 0.2

(iii) Probability of a helicopter door produced by Plant 1 given that the door is defective is:

a. 0.0001

b. 0.5

c. 0.002

d. 0.2 * 0.0001

Solutions

Expert Solution

ANSWER:

Given Information,

  • Doors Produced by Plant 1 = 1000 units
  • Doors Produced by Plant 2 = 4000 units
  • Overall defective doors percentage = 0.01% = 50 units
  • Defective percentage by plant 1 from overall = 50% = 25 units
  • Defective percentage by plant 2 from overall = 50% = 25 units

(i). The a-priori probability of defective helicopter doors produced by Plant 1 is?

Answer: b. 0.5

Explanation: A Priori Probability = Desired Outcome(s)/The Total Number of Outcomes

P(Defective door by Plant 1) = 25/50 = 0.5

(ii). Probability of helicopter doors produced by Plant 1?

Answer: d. 0.2

Explanation: Probability = Observed Outcome(s)/The Total Number of Outcomes

P(helicopter doors produced by Plant 1) = 1000/5000 = 0.2

(iii). Probability of a helicopter door produced by Plant 1 given that the door is defective is?

Answer: b. 0.5

Explanation:

  • P(A|B) – the probability of event A occurring, given event B has occurred
  • P(B|A) – the probability of event B occurring, given event A has occurred
  • P(A) – the probability of event A
  • P(B) – the probability of event B

Here, P(A) = Probablity of helicopter door produced by Plant 1 = 0.2

P(B) = Probablity the door is defective = 0.01

P(B|A) = Probablity that door is defective, given produced by Plant 1 = 25 / 1000 = 0.025

venereology answered 1 year ago
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