Ridss wrote:
A certain product must be subjected to (and pass) a sequence of various combinations of 5 tests (Tests A through E) before it may receive one of two certifications (Certification 1 or Certification 2). The diagram shows how products proceed through these tests, along with the probability of proceeding from each test to the next test or certification. For instance, the diagram shows that an item subjected to Test A has a 0.20 probability of passing Test A and being subjected to Test B next, a 0.75 probability of passing Test A and being subjected to Test C next, and a 0.05 probability of failing Test A. The probability that an item receives either of the two certifications is exactly 0.93.
Based on the information provided, select from each drop-down menu the option that creates the most accurate statement.
To the nearest hundredth, the probability that a randomly selected product subjected to Test A will receive Certification 1 is [dropdown1]
To the nearest hundredth, the probability that a randomly selected product subjected to Test A will receive Certification 2 is [dropdown2]
options : 0.86 , 0.91
Correct Answer:
Dropdown 1: 0.02
Dropdown 2: 0.91
For Question 1,
Probability of Test A receiving Certificate 1 will only have 1 path:
A --> B --> D --> Certificate 1= 0.2 * 0.2 * 0.5 =
0.020For Question 2,
Probability of Test A receiving Certificate 2 will only have 4 paths:
A --> C --> E --> Certificate 2 = 0.75 * 0.25 * 1.00 = [3][/16]
A --> C --> Certificate 2 = 0.75 * 0.75 = [9][/16]
A --> B --> E --> Certificate 2 = 0.2 * 0.7 * 1.00 = [7][/50]
A --> B --> D --> Certificate 2 = 0.2 * 0.2 * 0.5 = [1][/50]
Adding the probability of all possible paths,
[3][/16] + [9][/16] + [7][/50] + [1][/50] = [12][/16] + [8][/50] = [91][/100] =
0.91