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A packet of 10 electronic components is known to include 2 defectives. If a sample of 4 components is selected at random from the packet, what is the probability that the sample does not contain more than 1 defective?
  • a)
    1/3
  • b)
    2/3
  • c)
    13/15
  • d)
    3/15
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A packet of 10 electronic components is known to include 2 defectives....
Problem: Finding the probability of selecting a sample of 4 components from a packet of 10 electronic components that does not contain more than 1 defective.

Solution:
Let us first find the probability of selecting a sample of 4 components that contains no defectives.
Number of ways of selecting 4 components from 8 non-defective components = 8C4
Number of ways of selecting 4 components from 10 components = 10C4
Probability of selecting a sample of 4 components that contains no defectives = 8C4/10C4

Now, let us find the probability of selecting a sample of 4 components that contains exactly 1 defective.
Number of ways of selecting 1 defective component from 2 defective components = 2C1
Number of ways of selecting 3 non-defective components from 8 non-defective components = 8C3
Number of ways of selecting 4 components from 10 components = 10C4
Probability of selecting a sample of 4 components that contains exactly 1 defective = (2C1 x 8C3)/10C4

Therefore, the probability of selecting a sample of 4 components that does not contain more than 1 defective = Probability of selecting a sample of 4 components that contains no defectives + Probability of selecting a sample of 4 components that contains exactly 1 defective
= (8C4/10C4) + (2C1 x 8C3)/10C4
= 13/15

Hence, the correct answer is option 'C', 13/15.
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Community Answer
A packet of 10 electronic components is known to include 2 defectives....
13/15
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A packet of 10 electronic components is known to include 2 defectives. If a sample of 4 components is selected at random from the packet, what is the probability that the sample does not contain more than 1 defective?a)1/3b)2/3c)13/15d)3/15Correct answer is option 'C'. Can you explain this answer?
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