Wonky planes

What this plane-safety probability question tests

This is an easy probability problem that asks you to compare the failure rates of two aircraft designs using binomial reasoning. It appears frequently in quant interviews because it requires you to set up and solve a simple equation, then reason about whether one design dominates the other across all parameter values.

To approach it, calculate the probability that each plane type fails (given the failure probability of individual engines and the redundancy structure), then find the value of the engine failure rate at which the two probabilities are equal. Next, determine whether one plane is uniformly safer by comparing their failure curves across the full range of possible engine reliabilities.

• Binomial distribution and tail probabilities
• Comparing competing failure modes
• Reasoning about parameter sensitivity and stochastic dominance