Solution
Shooting Stars
Show the problem again
The probability of seeing at least one shooting star during any given hour is 0.84. Assuming shooting stars appear independently over time at a constant rate, what is the probability of seeing at least one during a 10-minute interval? Round to 3 decimal places.
Worked solution
The answer is 1 − 0.16^(1/6) ≈ 0.263. The probability of seeing none in an hour is 0.16. An hour is six independent 10-minute blocks, so if q is the probability of seeing none in 10 minutes, q⁶ = 0.16, giving q = 0.16^(1/6) ≈ 0.737. So P(at least one) ≈ 0.263. A common trap is answering 0.84/6 = 0.14.
Source: Standard Poisson-process exercise from introductory probability texts. Statement written for AxiomIQ.