Artificial intelligent assistant

Why taking a bomb with you to the airplane won't improve your chances of survival There was an old woman, who had to take a flight for the first time and she was terrified of the prospect that someone had a bomb there, so she called the company and asked how likely it was that there was a bomb. Extremely small, the company answered. The woman then asked, how likely it was that there are two bombs. Far far more unlikely than that there was only one bomb, they answered. So the woman went on the flight with a bomb. Prove logically that this reasoning is not valid.

The events are (presumably) independent: $$\mathrm{Pr}[\text{someone else having a bomb}]=\mathrm{Pr}[\text{someone else having a bomb}|\text{old woman has a bomb}].$$

The fact that the old woman has a bomb makes no difference to the probability of someone else having a bomb (unless, say, she happens to be with a terrorist organisation and tends to fly with other terrorists).

xcX3v84RxoQ-4GxG32940ukFUIEgYdPy 8618d820ba284590c379957b4fe88130