suppose I am going to toss a coin of diameter 1 inch in a square box that has length of 2 inch .Whats the probability of the coin dropping in the box but will not touch the border?

  • $\begingroup$ What have you tried? Please show your efforts at solving the problem. $\endgroup$ – Varun Vejalla Feb 23 at 16:19
  • $\begingroup$ area of coin/area of box $\endgroup$ – Tekton_infernus Feb 23 at 16:21
  • $\begingroup$ @Tekton_infernus : favourable area / total area $\endgroup$ – tommik Feb 23 at 16:22
  • 2
    $\begingroup$ This is horribly underspecified. With what probability distribution and what sample space does the coin enter the box? A highly precise robot can with $100\%$ accuracy land the coin in the box without touching the edges every single time. A small child on the other hand might not even successfully get the coin in the box when trying... $\endgroup$ – JMoravitz Feb 23 at 16:24
  • 1
    $\begingroup$ And what happens near the corners? If the centre of the coin is just inside the corner, almost 3/4 of the coin is outside the edges of the box. Does it go in or not? $\endgroup$ – Jaap Scherphuis Feb 23 at 16:27

With a simple drawing you realize that the probability is


enter image description here

that is the area of the red square divided by the total area

  • 1
    $\begingroup$ This makes wild unjustified assumptions as to the probability distribution at play here. $\endgroup$ – JMoravitz Feb 23 at 16:26
  • $\begingroup$ @JMoravitz ...assuming uniform distribution in the square $\endgroup$ – tommik Feb 23 at 16:27
  • $\begingroup$ @tommik thats the answer I was looking for,thanks $\endgroup$ – Tekton_infernus Feb 23 at 16:28
  • 1
    $\begingroup$ There are two outcomes when playing the lottery, you either win or you lose. You do not win half of the time however. $\endgroup$ – JMoravitz Feb 23 at 16:33
  • 1
    $\begingroup$ The probability given in this answer assumes that the center of the coin always lands uniformly over the interior of the box and only over the interior of the box. My guess would be that the distribution of where the center of the coin lands would tend to be a normal distribution, not uniformly within a sharp square. $\endgroup$ – robjohn Feb 23 at 21:32

Not the answer you're looking for? Browse other questions tagged or ask your own question.