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-correct means that it outputs the correct answer with probability at least<img alt="p" src="https://XXXXX.XXXXXXXX.XXX/media/XXX/XXXXXXXX-XXXX-4011-XXXX-2214b1d144e9/XXXXXXXX-XXXX-4e7f-XXXX-d7dd933ed1e1.XXX" XXXX-describedby="he1" style="margin: 0px; padding: 0px; border: XXX; XXXX: inherit; vertical-XXXXX: XXXXXXXX; XXX-width: 100%; XXXXXX: auto;">i.e. a true-XXXXXX XXXXXXXXX XXXX XXXXXX true with XXXX probability and similarly a false-biased XXXXXXXXX XXXX output XXXXX with XXXX XXXXXXXXXXX. X XXX Vegas XXXXXXXXX can output<XXX alt="?" XXX="XXXXX://XXXXX.XXXXXXXX.com/XXXXX/689/689378a9-7db4-458c-a5fe-1b8730058f6e/8b619afb-XXXX-XXXX-ba8e-4fa2c7b2f1a5.XXX" XXXX-describedby="he3" style="XXXXXX: 0px; padding: 0px; border: XXX; XXXX: inherit; XXXXXXXX-align: XXXXXXXX; max-width: 100%; XXXXXX: auto;">or<img XXX="XXXX" src="XXXXX://XXXXX.cheggcdn.XXX/media/XXX/a38c6391-XXXX-4fdf-XXXX-07b7c92720db/7c7ca88f-6f90-XXXX-b8fd-4dd9d155e7cb.png" XXXX-describedby="XXX" style="XXXXXX: XXX; padding: XXX; border: XXX; XXXX: inherit; vertical-XXXXX: baseline; XXX-width: XXX%; height: XXXX;">, XXX if it XXXXXXXX an output, it must XXXXXXX XXX XXXXXXX XXXXXX.</p> <p>XXX idea to XXXXXX a Las XXXXX algorithm XXXX two XXXXX carlo XXXXXXXXXX, one XX XXXXX XX XXXX-XXXXXX and XXX XXXXX XXX XXXXX-biased, XX as XXXXXXX.</p> <p>First XXX XXX XXXXXXXXX A. XX it output XXXX, output XXXX, which is XXXXXXXXXX XX XXXXXXX XX X is XXXX-XXXXXX. Otherwise, XXX algorithm B and if it XXXXXXX XXXXX, XXXXXX false, XXXXX XX XXXXX guaranteed to XX XXXXXXX because B is false-biased. XX X XXXXX't output true, and B doesn't XXXXXX XXXXX, output<img alt="?" XXX="https://XXXXX.cheggcdn.com/media/XXX/XXXXXXXX-XXXX-XXXX-a5fe-1b8730058f6e/XXXXXXXX-XXXX-499b-ba8e-4fa2c7b2f1a5.png" aria-describedby="XXX" style="margin: XXX; padding: XXX; border: 0px; XXXX: inherit; XXXXXXXX-XXXXX: baseline; max-width: XXX%; XXXXXX: XXXX;">, which XX that XXX XXXXXXXXX has failed XX find the correct answer.</p> <p>XXX XXXXX time XXXX takes XX, one XXXX XXX A, XXX call XXX X, and XXXX small additional XXXX XXX XXXXXXXXXXX.</p> <p>To XXXXXXXXX the XXXXXXX probability, notice that the algorithm succeeds XX X XXXXXXX XXXX, or XX A outputs false and XXXX B XXXXXXX XXXXX. XXX former XXXXXXX XXXX probability<XXX alt="p" XXX="XXXXX://media.XXXXXXXX.XXX/XXXXX/646/6468bebb-XXXX-4011-XXXX-2214b1d144e9/e9a696b2-XXXX-XXXX-9f22-XXXXXXXXXXXX.png" XXXX-describedby="XXX" style="margin: 0px; padding: 0px; border: 0px; font: inherit; vertical-XXXXX: XXXXXXXX; max-width: 100%; XXXXXX: auto;">, XXXXX the latter happens XXXX XXXXXXXXXXX<img XXX="(X-p)q" src="XXXXX://media.cheggcdn.com/media/XXX/XXXXXXXX-XXXX-4ae7-829e-XXXXXXXXXXXX/ece2cc79-XXXX-4827-84f6-XXXXXXXXXXXX.XXX" aria-XXXXXXXXXXX="he7" style="XXXXXX: 0px; padding: 0px; border: 0px; XXXX: inherit; vertical-align: XXXXXXXX; max-width: XXX%; height: auto;">. XXXXX,<XXX XXX="r = p + (X-p)q" src="XXXXX://media.XXXXXXXX.XXX/media/3e9/XXXXXXXX-f2fa-4521-aa16-372727854cf0/XXXXXXXX-XXXX-XXXX-XXXX-9a99da924833.XXX" aria-describedby="he8" style="XXXXXX: 0px; padding: 0px; border: XXX; XXXX: inherit; vertical-XXXXX: XXXXXXXX; max-width: 100%; XXXXXX: XXXX;">.</p><p><br></p>">
