Bayesian Updating A rider is waiting for a bus and the bus is always X hours late.

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Question:

Bayesian Updating

A rider is waiting for a bus and the bus is always X hours late. X is a random variable distributed uniformly on a range [0, A]. A priory it is known that A is equal to any one of the
following values with equal probability: (1/6), (1/4), (1/3), (1/2). If the bus arrives 12 minutes late (1/5 of an hour), what is the posterior probability for the most likely value of A?

Choices:

5/7
4/9
3/4
1/2

Give a detailed explanation.