I used to get this problem with defensive systems: an 85% probability of stopping a Bad Thing from hitting you, sounds great and arguing that we really needed it up in the high 90s, was a hard sell - isn't 85% "really good" already?
Since the probability was about right, and the consequence of being hit was "really bad", I found using the Mess Webley analogy - one revolver, one round loaded, one game of Russian Roulette, per incoming threat - really helped to clarify it.
Salvo of four incoming? Spin the cylinder, put the gun to your head, pull the trigger. Repeat three more times. Still think those odds are good enough? Put the extra bit of kit I'm arguing for on the ship, and now the odds for a salvo of four are better than "one gun, one bullet, one game". [1]
Describe it like that, and I got more buy-in for "okay, maybe that extra defensive layer you want is a good investment after all..." where trying to explain "four consecutive 85% probabilities of not getting hit, mean it's only fifty-fifty whether you survive..." just didn't seem to get traction.
[1] Let's not get into the Bayesian probability / Monty Hall Effect of whether you should, or shouldn't, spin the cylinder between each game, or we'll be here all week...