Answer:
To find the probability that none of the six independent field joints failed, we need to use the rule of multiplication, which states that the probability of two independent events occurring together is the product of their individual probabilities.
Let's assume that the probability of a field joint failing is p. Since there are six independent field joints, the probability that none of them fail is:
P(0) = (1-p) * (1-p) * (1-p) * (1-p) * (1-p) * (1-p)
This is because the probability of each field joint not failing is (1-p), and since the field joints are independent, we can multiply their individual probabilities to get the probability that none of them fail.
Simplifying the expression, we get:
P(0) = (1-p)⁶
Therefore, the rule of multiplication was used to find P(0), the probability that none of the six independent field joints failed