On a deserted road, the probability of observing a car during a thirty-minute period is 95%.
What is the chance of observing a car in a ten-minute period?

Hint: To clarify the question we are saying the probability of seeing any other cars in 30 minutes is 95% or more clearly, and more usefully, the probability of not seeing any other cars is 5%.

  • $\begingroup$ btw how you put spoiler box? $\endgroup$ – Juan Carlos Oropeza Jan 28 '15 at 18:42
  • $\begingroup$ You can use >! to hide spoilers $\endgroup$ – dmg Jan 28 '15 at 19:22
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    $\begingroup$ I believe this question is not on-topic here because it is a math problem, not a math puzzle, as per meta discussion. It should instead go on math.SE. $\endgroup$ – xnor Jan 29 '15 at 3:26
  • $\begingroup$ I understand why you may see it as a just a math problem, for me because I not enter in the probabality field frequently, the solution was nice. I only could solve this problem when I realize the similitud to solve the problem probabilty of have 3 head coin toss in a row that was my eureka moment for the day. $\endgroup$ – Juan Carlos Oropeza Jan 29 '15 at 4:32

The answer is:

100% - 5%^(1/3) (cube root of 5%), which is about 63%


Because the probability of not seeing a car in thirty minutes is equal to the probability of not seeing a car for ten minutes to the third power. That is, not seeing a car for ten minutes three times in a row is like not seeing a car for thirty minutes

Or, with a formula:

If $P_{not30}$ is the probability of not seeing a car for 30 minutes and $P_{not10}$ is the probability of not seeing a car for ten minutes, $P_{not30}$= $P_{not10}^ 3 \Rightarrow$ $P_{not10} = \sqrt[3]{P_{not30}}$

  • $\begingroup$ just showing powers,cubes is not useful explain with numbers :) $\endgroup$ – iOSdev Jan 30 '15 at 10:36
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    $\begingroup$ @user232783 What do you mean? This: 1 - cube_root(0.05) ~= 1 - 0.3684031498640387 = 0.6315968501359612 ~= 0.63 = 63%? $\endgroup$ – dmg Jan 30 '15 at 10:39
  • $\begingroup$ ok i understood ur answer now.. thanks $\endgroup$ – iOSdev Jan 30 '15 at 10:40

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