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The probability of a defective piece being produced in a manufacturing process is 0.01. The probability that out of 5 successive pieces, only one is defective, is
- a)(0. 99)2 (0.01)
- b)(0.99)( 0.01)4
- c)5× (0.99)(0.01)4
- d)5× (0.99)4(0.01)
Correct answer is option 'D'. Can you explain this answer?
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Probability of a Defective Piece
To begin with, the probability of a defective piece being produced is given as 0.01.
Probability of Only One Defective Piece in 5 Successive Pieces
Now, we need to find the probability that out of 5 successive pieces, only one is defective. This can be calculated using the binomial distribution formula:
P(X = k) = nCk * pk * (1-p)n-k
where,
n = number of trials
k = number of successful trials
p = probability of success
1-p = probability of failure
In this case, we have:
n = 5 (since we have 5 successive pieces)
k = 1 (since we want only one to be defective)
p = 0.01 (since the probability of a defective piece is 0.01)
1-p = 0.99 (since the probability of a non-defective piece is 0.99)
Therefore, the probability of only one defective piece in 5 successive pieces is:
P(X = 1) = 5C1 * (0.01)1 * (0.99)4
= 5 * 0.01 * 0.96059601
= 0.048028
Answer
Hence, the correct answer is option 'D', which is 5 (0.99)4(0.01).
To begin with, the probability of a defective piece being produced is given as 0.01.
Probability of Only One Defective Piece in 5 Successive Pieces
Now, we need to find the probability that out of 5 successive pieces, only one is defective. This can be calculated using the binomial distribution formula:
P(X = k) = nCk * pk * (1-p)n-k
where,
n = number of trials
k = number of successful trials
p = probability of success
1-p = probability of failure
In this case, we have:
n = 5 (since we have 5 successive pieces)
k = 1 (since we want only one to be defective)
p = 0.01 (since the probability of a defective piece is 0.01)
1-p = 0.99 (since the probability of a non-defective piece is 0.99)
Therefore, the probability of only one defective piece in 5 successive pieces is:
P(X = 1) = 5C1 * (0.01)1 * (0.99)4
= 5 * 0.01 * 0.96059601
= 0.048028
Answer
Hence, the correct answer is option 'D', which is 5 (0.99)4(0.01).
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