7
$\begingroup$

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%.

$\endgroup$

closed as off-topic by xnor, mdc32, Tryth, McMagister, BmyGuest Jan 31 '15 at 16:32

  • This question does not appear to be about creation and solving of puzzles, within the scope defined in the help center.
If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ 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
  • 7
    $\begingroup$ 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
7
$\begingroup$

The answer is:

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

Why?

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, $P_{not30}$= $P_{not10}^ 3 \Rightarrow$ $P_{not10} = \sqrt[3]{P_{not30}}$

$\endgroup$
  • $\begingroup$ just showing powers,cubes is not useful explain with numbers :) $\endgroup$ – iOSdev Jan 30 '15 at 10:36
  • 1
    $\begingroup$ @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

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