Answer Happy

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? (e) 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?