The table below gives the number of components in boxes A , B and C and how many
ID: 3358157 • Letter: T
Question
The table below gives the number of components in boxes A, B and C and how many of these components are defective in each one.
Box
A component is chosen at random from one of the boxes. What is the probability that the chosen component is from box A (P(A))? What is the probability that the chosen component is defective (P(D))?What is the probability that the component is from box A if it is defective (P(A|D))?
Write correct answers to 3 significant figures.
Box
A B C No. of components in box 300 200 100 No. of defectives in box 15 10 12Explanation / Answer
Total number of components = 300 + 200 + 100 = 600
a) Probability that the chosen component is from box A is computed as:
= Number of components in box A / Total number of components
= 300/600
= 0.5
Therefore 0.500 is the required probability here.
b) Total number of defectives = 15 + 10 + 12 = 37
Therefore the probability that the chosen components is defective is computed as:
= Total number of defectives / Total number of components
= 37/600
= 0.0617
Therefore 0.062 is the required probability here.
c) Given that a components is defective, probability that it is from box A is computed as:
= Number of defective components from box A / Total number of defectives
= 15 / 37
= 0.405
Therefore 0.405 is the required probability here.
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