If a car has a 90% chance of starting in the morning, what is the probability it will start every morning over a 5-day workweek?

Instruction: Assume five independent morning outcomes, each with a 90% chance of the car starting. Calculate the all-five probability and explain why independence cannot be inferred from the daily rate alone.

Context: This question assesses the candidate's understanding of probability in sequential events and their ability to calculate the probability of repeated successes.

Updated

Official answer

If each morning's starting outcome is independent of the others and has success probability 0.9, then P(starts all five mornings) = 0.9^5 = 0.59049, or 59.049%.

Independence is additional information, not a consequence of a 90% marginal rate. For example, if a persistent condition makes all five outcomes identical, a 90% chance of that condition being favorable gives a 90% chance of all five starts. Battery condition or weather may create dependence in a real car.

The general calculation multiplies the first success probability by successive probabilities conditional on all previous successes. Under the independent model, each factor is 0.9.

Related Questions