Probability problems on Loom

Question

A loom experiences one yarn breakage approximately every $10$ hours. A particular style of cloth is being produced that will take $25$ hours on this loom. If $3$ or more breaks are required to render the product unsatisfactory, find the probability that the style of cloth is finished with acceptable quality.

Answer 1

If the first breakage occurs in the first $5$ hours, The Product is unsatisfactory. Else, it is good.

The first break can occur in any of the first $10$ hours with equal probability. So, The probability I say is $1\over 2$.

Answer 2

If you model this on a Poisson process, the average number of breaks in a $25$ hour period is $\lambda=2.5$ and the probability of getting exactly $k$ breaks in the period is $$P(k)=\frac {\lambda^ke^{-\lambda}}{k!}$$ The answer is then $$P(0)+P(1)+P(2)\sim .5438$$