A person jumps from a very slow moving train. Let A be the event that he survives, and B be the event that he does not survive. Then which one of the following statements describes the events A and B most appropriately?

The answer is mutually exclusive, exhaustive, but not equally likely

I got this answer wrong. I am told the since the train is slow moving, the events are NOT equally likely. But I differ on this. For me, I chose the inputs on outcomes 1>Survives 2> Does not Survive. attaching the probability is 50%. The movement we focus on "slow moving" train - I feel we are subjective....further I can argue the slow moving train on a bridge vs on ground can have different outcomes :)

Am i not right ? should'nt the answer be Mutually exclusive, Exhaustive, Equally Likely - psl clarify

  • 2
    $\begingroup$ It is a common mistake to assess a situation where two outcomes are possible as if the two outcomes are equally likely. This very rarely happens, generally only with tightly-constrained events that are artificially set up to produce those balanced outcomes. $\endgroup$
    – Joffan
    Sep 5, 2017 at 7:52

1 Answer 1


Why would you assume equally likely? That would mean a 50% chance of not surviving. How would you justify that number? Exactly 50%? Not 51%, or 49%, or some other number?

I agree that there's not enough information to conclude that $A,B$ are not equally likely, but given the choices, even without knowing the speed of the train, the claim "exactly 50%" is a less natural choice than the claim "not exactly 50%".

But to help you make the choice, they described the train as not just "slow moving", but "very slow moving". That would mean, from a common sense perspective, that the jumper would need to be very unlucky to not survive.

Inventing bridges is not justified. You should assume just the given info with default settings for information not provided.

That said, I don't like the choices offered, precisely since it requires real-world-most-likely-case judgement, as opposed to mathematical reasoning.

Nevertheless, if I was faced with that question under test conditions, I would choose the answer which the test "wanted", so I would have gotten it "right".


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