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S2, continuous uniform distribution

A piece of spaghetti has length 2c, where c is a positive constant. It is cut into two pieces
at a random point. The continuous random variable X represents the length of the longer
piece and is uniformly distributed over the interval [c, 2c].

Find the probability that the longer piece is more than twice the length of the shorter
piece.

could someone please explain the answer to this question
So think about the piece of spaghetti, if the longer piece is twice the length of the shorter, then that is a ratio 2:1, and so it will be greater than 2/3 the total length length.
Of course you will need to consider when one piece is longer OR when the other piece is longer too, and subsequently find the resultant probability.
Original post by Hafsahk
A piece of spaghetti has length 2c, where c is a positive constant. It is cut into two pieces
at a random point. The continuous random variable X represents the length of the longer
piece and is uniformly distributed over the interval [c, 2c].

Find the probability that the longer piece is more than twice the length of the shorter
piece.

could someone please explain the answer to this question


Original post by UncookedYogurt
So think about the piece of spaghetti, if the longer piece is twice the length of the shorter, then that is a ratio 2:1, and so it will be greater than 2/3 the total length length.
Of course you will need to consider when one piece is longer OR when the other piece is longer too, and subsequently find the resultant probability.


This is a duplicate of https://www.thestudentroom.co.uk/showthread.php?t=5447476

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