What is the probability of hitting the line?

We have a line drawn in the floor, say 100 cm. This line color was blue. Another man came and drew a short line randomly on our line and in red, say the length of that line is 5 cm.

We have a piece of metal that falls randomly on that line. It is clear that this piece probability to fall on the red line is 5%

My question

What if we have $$2$$ pieces? What is the probability of at least one of them hit the red line ? And how it get calculated?

What if we have $$3$$ or $$N$$ pieces then what is the probability at least one of them hit the line?

My attempt was like following:

$$p(x) = 0.05$$

the probability of double event is $$0.05 \cdot 0.05$$ which is $$0.0025$$ which is wrong for sure. The probability has to increase not decrease.

Thanks

• Try to calculate first that you won't hit once in N attempts. Commented Apr 28, 2019 at 5:53
• look up binomial experiment. In your case $n$ is the number of pieces, $p=0.05$ is the probability of success and you need to find $\mathbb P(X\ge 1)=1-\mathbb P(X=0)$. Commented Apr 28, 2019 at 10:03
• @farruhota thanks, this equation is what i need P(X≥1)=1−P(X=0). Commented Apr 28, 2019 at 10:10