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-correct means that it outputs the correct answer with probability at least<img alt="p" src="https://media.XXXXXXXX.XXX/media/XXX/XXXXXXXX-XXXX-4011-XXXX-XXXXXXXXXXXX/e9a696b2-XXXX-4e7f-XXXX-XXXXXXXXXXXX.png" aria-XXXXXXXXXXX="XXX" style="XXXXXX: XXX; padding: 0px; border: 0px; XXXX: inherit; vertical-XXXXX: XXXXXXXX; max-width: 100%; height: auto;">i.e. a XXXX-biased XXXXXXXXX XXXX output true with XXXX probability and similarly a false-biased algorithm XXXX XXXXXX XXXXX with this probability. A Las Vegas algorithm XXX output<XXX XXX="?" XXX="XXXXX://media.XXXXXXXX.com/XXXXX/XXX/XXXXXXXX-XXXX-458c-a5fe-1b8730058f6e/XXXXXXXX-26f7-499b-XXXX-4fa2c7b2f1a5.XXX" XXXX-describedby="XXX" style="XXXXXX: XXX; padding: 0px; border: 0px; font: inherit; XXXXXXXX-XXXXX: XXXXXXXX; XXX-width: 100%; height: auto;">or<img alt="fail" XXX="https://XXXXX.cheggcdn.XXX/media/a38/a38c6391-e78d-XXXX-XXXX-XXXXXXXXXXXX/7c7ca88f-6f90-XXXX-XXXX-4dd9d155e7cb.XXX" aria-XXXXXXXXXXX="XXX" style="margin: XXX; padding: XXX; border: XXX; font: inherit; XXXXXXXX-XXXXX: XXXXXXXX; XXX-width: 100%; height: auto;">, but if it XXXXXXXX an XXXXXX, it must produce the XXXXXXX output.</p> <p>XXX XXXX to XXXXXX a XXX XXXXX algorithm XXXX two Monte XXXXX XXXXXXXXXX, XXX of XXXXX XX true-XXXXXX and the other one XXXXX-biased, XX XX XXXXXXX.</p> <p>First XXX XXX XXXXXXXXX A. If it output XXXX, output true, which XX guaranteed XX correct as X XX XXXX-XXXXXX. XXXXXXXXX, run algorithm B XXX XX it outputs false, output false, XXXXX XX again XXXXXXXXXX XX XX XXXXXXX XXXXXXX X is false-XXXXXX. If A XXXXX't XXXXXX XXXX, and X doesn't XXXXXX XXXXX, XXXXXX<img alt="?" src="XXXXX://media.XXXXXXXX.com/XXXXX/689/XXXXXXXX-XXXX-458c-XXXX-XXXXXXXXXXXX/8b619afb-26f7-499b-XXXX-4fa2c7b2f1a5.XXX" aria-describedby="he3" style="margin: 0px; padding: 0px; border: XXX; font: inherit; vertical-XXXXX: baseline; XXX-width: XXX%; height: auto;">, which XX XXXX the XXXXXXXXX XXX XXXXXX XX XXXX XXX correct answer.</p> <p>XXX XXXXX XXXX this XXXXX is, one call for X, XXX XXXX for X, and some XXXXX additional XXXX XXX XXXXXXXXXXX.</p> <p>To calculate XXX XXXXXXX XXXXXXXXXXX, notice XXXX the XXXXXXXXX XXXXXXXX if A XXXXXXX XXXX, or if X XXXXXXX false and then X XXXXXXX XXXXX. XXX XXXXXX happens with probability<XXX alt="p" src="XXXXX://XXXXX.XXXXXXXX.com/XXXXX/646/6468bebb-a9ce-4011-a103-2214b1d144e9/e9a696b2-edc0-4e7f-XXXX-d7dd933ed1e1.XXX" aria-XXXXXXXXXXX="he6" style="XXXXXX: 0px; padding: XXX; border: XXX; font: inherit; vertical-XXXXX: XXXXXXXX; max-width: XXX%; XXXXXX: auto;">, while XXX XXXXXX XXXXXXX XXXX XXXXXXXXXXX<img alt="(1-p)X" XXX="https://XXXXX.XXXXXXXX.com/XXXXX/fc2/XXXXXXXX-6c47-XXXX-829e-38a7afe6840d/ece2cc79-XXXX-XXXX-84f6-e287ac93562a.png" XXXX-describedby="XXX" style="XXXXXX: 0px; padding: 0px; border: XXX; XXXX: inherit; vertical-align: XXXXXXXX; XXX-width: 100%; height: XXXX;">. Hence,<img alt="r = p + (X-p)q" src="https://XXXXX.XXXXXXXX.XXX/media/XXX/3e9bf3b4-XXXX-4521-aa16-372727854cf0/XXXXXXXX-XXXX-4ae0-951a-9a99da924833.XXX" aria-describedby="he8" style="margin: 0px; padding: 0px; border: 0px; font: inherit; vertical-align: XXXXXXXX; max-width: 100%; height: auto;">.</p><p><XX></p>">
