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A box consists of 14 components, 5 of which are defective.
(a) Components are selected and tested one at a time, without replacement, until a non-defective component is
found. Let X be the number of tests required. Find P(X= 5).
(b) Components are selected and tested, one at a time without replacement, until two consecutive non defective
components are obtained. Let X be the number of tests required. Find P(X= 5).


what is process of getting solution ​

Answer :

Answer:

a) Find P(X= 5) = 0.0004995

b) Find P(X= 5) = 0.0243

Step-by-step explanation:

The detailed steps and analysis is as shown in the attached file.

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The probability of making selections without replacement to obtain the required events are :

  • P(X = 5) = 0.0045

  • P(X=5) = 0.0180

  • Total number of components = 14

  • Number of defective components, D = 5

  • Number of non-defective components, N = 9

1.)

Probability that 5 components are selected until a non-defective item is selected :

  • D, D, D, D, N

P(DDDDN) = (5/14) × (4/13) × (3/12) × (2/11) × (9/10) = 0.0045

2.)

Probability that 5 components are selected until 2 consecutive non-defective components are obtained :

  • D, D, D, N, N

P(DDDNN) = (5/14) × (4/13) × (3/12) × (9/11) × (8/10) = 0.0180

Therefore, the required probabilities are 0.0045 and 0.0180 respectively.

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