mathematics - Probability of Seeing a Car in 10 Minutes & 30 Minutes

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%.

Answer

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