Zholtan is a civil engineer. He is alarmed by a report that a bridge in a nearby town recently collapsed. This is an unusual event, but he knows that it is far from impossible; nationwide statistics show that one in ten bridges are in urgent need of repair because they are structurally unsound. The next day, while inspecting a bridge in his town, Zholtan noticed very small cracks called hairline cracks in one of the girders of the bridge. This is an early sign of serious trouble. All bridges that are structurally unsound show some hairline cracking. However, Zholtan knows that 75% of bridges that never collapse also have hairline cracked foundations.

Numerically, how confident should Zholtan be that this bridge is structurally unsound? Show your calculations.

Suppose that when a bridge is structurally unsound it costs $1MM (one million dollars) to close the bridge and repair it now,or $10MM not to close it, for the damage will become worse and more work will be needed later. If the bridge is sound and is not closed the city would not lose any money, but if a sound bridge is closed then the city would lose $100k (one hundred thousand dollars) because the workers' time would be wasted. After having seen the hairline cracking, should Zholtan close the bridge for repairs?