6. In all the state of the union (SOTU) addresses since that of President George Washington in the year 1790 to that of President Barack Obama in the year 2016, a total of 69,158 sentences were spoken. In all SOTU addresses following that of President Woodrow Wilson in 1920, a total of 32,752 sentences were spoken; among these, 15,934 had a length or 20 words or more. Among the sentences spoken prior to this, 27,639 had a length of 20 words or more. See https://doi.org/10.46430/phen0061 if you want to play with this kind of data. (a) If you select a sentence at random from the SOTU addresses given after 1920, with what probability does it have a length of at least 20 words? (b) If you select a sentence at random from the SOTU addresses given before or during 1920, with what probability does it have a length of at least 20 words? (c) If you select a sentence at random from all the SOTU addresses from 1790 to 2016, with what probability does it have a length of at least 20 words? (d) If you select a sentence at random from all the SOTU addresses from 1790 to 2016, what is the probability that it belongs to a SOTU address given after 1920, given that it has a length of at least 20 words?

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6. In all the state of the union (SOTU) addresses since that of President George Washington in the
year 1790 to that of President Barack Obama in the year 2016, a total of 69,158 sentences were
spoken. In all SOTU addresses following that of President Woodrow Wilson 1920, a total of
32,752 sentences were spoken; among these, 15,934 had a length or 20 words or more. Among the
sentences spoken prior to this, 27,639 had a length of 20 words or more.
See https://doi.org/10.46430/phen0061
if you want to play with this kind of data.
(a) If you select a sentence at random from the SOTU addresses given after 1920, with what
probability does it have a length of at least 20 words?
(b) If you select a sentence at random from the SOTU addresses given before or during 1920, with
what probability does it have a length of at least 20 words?
(c) If you select a sentence at random from all the SOTU addresses from 1790 to 2016, with what
probability does it have a length of at least 20 words?
(d) If you select a sentence at random from all the SOTU addresses from 1790 to 2016, what is
the probability that it belongs to a SOTU address given after 1920, given that it has a length
of at least 20 words?
Page 2
Transcribed Image Text:6. In all the state of the union (SOTU) addresses since that of President George Washington in the year 1790 to that of President Barack Obama in the year 2016, a total of 69,158 sentences were spoken. In all SOTU addresses following that of President Woodrow Wilson 1920, a total of 32,752 sentences were spoken; among these, 15,934 had a length or 20 words or more. Among the sentences spoken prior to this, 27,639 had a length of 20 words or more. See https://doi.org/10.46430/phen0061 if you want to play with this kind of data. (a) If you select a sentence at random from the SOTU addresses given after 1920, with what probability does it have a length of at least 20 words? (b) If you select a sentence at random from the SOTU addresses given before or during 1920, with what probability does it have a length of at least 20 words? (c) If you select a sentence at random from all the SOTU addresses from 1790 to 2016, with what probability does it have a length of at least 20 words? (d) If you select a sentence at random from all the SOTU addresses from 1790 to 2016, what is the probability that it belongs to a SOTU address given after 1920, given that it has a length of at least 20 words? Page 2
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