Final answer:
To find the probability of no flaws in a 10 meter long cloth, we calculate the probability of no flaw per meter (19/20) and raise it to the power of 10. The result of this calculation yields the probability of no flaws in 10 meters.
Step-by-step explanation:
The question asks us to calculate the probability that there are no flaws in a 10 meters long cloth when it is known that a certain loom produces one flaw every 20 meters in the cloth it weaves. Since the flaws occur randomly, this scenario can be treated as a geometric distribution problem.
To find the probability of no flaws in 10 meters, we first find the probability of a flaw occurring per meter, which is 1 flaw per 20 meters. The probability of no flaw occurring in one meter then is 1 - (1/20) = 19/20. Since we want to find the probability of no flaws in 10 consecutive meters, we raise the probability of no flaw in one meter to the power of 10.
Probability of no flaws in 10 meters = (19/20)^10
Thus, the probability that there are no flaws in a cloth that is 10 meters long is given by the expression (19/20)^10. Using a calculator, this calculation provides the required answer.