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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.

enter image description here 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

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    $\begingroup$ Try to calculate first that you won't hit once in N attempts. $\endgroup$
    – georg
    Commented Apr 28, 2019 at 5:53
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    $\begingroup$ 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 $\mathbb P(X\ge 1)=1-\mathbb P(X=0)$. $\endgroup$
    – farruhota
    Commented Apr 28, 2019 at 10:03
  • $\begingroup$ @farruhota thanks, this equation is what i need P(X≥1)=1−P(X=0). $\endgroup$
    – asmgx
    Commented Apr 28, 2019 at 10:10

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