Question

The probability of a defective piece being produced in a manufacturing proces is 0.01. The probability that out of 5 successive pieces, only one is defective, is

• A. $\left(0.99{)}^4\right(0.01)$
• B. $\left(0.99\right)(0.01{)}^4$
• C. $5\times \left(0.99\right)(0.01{)}^4$
• D. $5\times \left(0.99{)}^4\right(0.01)$

Answer 1

The correct option is D $5\times \left(0.99{)}^4\right(0.01)$

Probability of defective = 0.01
Probability of non-defective = 1 - 0.01 = 0.99
Probability that out of 5 successive pieces, only one is defective is

$P={}^5{C}_1\left(0.99{)}^4\right(0.01)$

$P=5{(0.99)}^4(0.01)$