Final answer:
The probability of a perfect order given 97% reliability on four attributes is calculated by multiplying the probability of success for each attribute. The result, rounded to four decimal places, is 0.8853.
Step-by-step explanation:
The question is asking for the probability of achieving a 'Perfect Order' when there is a 97% reliability on each of four separate attributes. In order to calculate this, we need to consider the probability of each attribute being successful and then multiply these probabilities together since each attribute is independent of the others.
The probability of each attribute being successful is 0.97. Since there are four independent attributes, we use the formula for the probability of independent events:
- P(A and B and C and D) = P(A) × P(B) × P(C) × P(D)
Substitute the probabilities into the equation:
P(Perfect Order) = 0.97 × 0.97 × 0.97 × 0.97
Calculate the combined probability:
P(Perfect Order) = 0.8853 (rounded to four decimal places)
Therefore, the probability of a perfect order given 97% reliability on four attributes is 0.8853.