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Консультация № 189099
05.04.2016, 18:13
0.00 руб.
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Производится стрельба по цели площадью 45 кв.м. одним снарядом. Цель состоит из трех частей, площади которых 10, 15 и 20 кв.м. При попадании в первую часть цель поражается с вероятностью 0,9, во вторую - 0,8, в третью - 0,7.
а) найти среднюю вероятность поражения цели;
б) известно, что цель поражена. Определите, в какую из частей цели вероятнее всего попал снаряд.
Производится стрельба по цели площадью 45 кв.м. одним снарядом. Цель состоит из трех частей, площади которых 10, 15 и 20 кв.м. При попадании в первую часть цель поражается с вероятностью 0,9, во вторую - 0,8, в третью - 0,7.
а) найти среднюю вероятность поражения цели;
б) известно, что цель поражена. Определите, в какую из частей цели вероятнее всего попал снаряд.
Обсуждение
05.04.2016, 19:59
общий
это ответ
Здравствуйте, Aleksandrkib!
Примем, что для попавшего в цель снаряда вероятность попасть в одну из частей цели пропорциональна площади части.
Сформулируем гипотезы и укажем их вероятности:
1)
- снаряд попал в первую часть. Вероятность равна 
2)
- снаряд попал во вторую часть. Вероятность равна 
3)
- снаряд попал в третью часть. Вероятность равна 
По формуле полной вероятности (средняя) вероятность поражения цели (события
) составляет
Пусть цель поражена. Вычислим условные вероятности попадания снаряда по формуле Байеса (теореме гипотез):
1) в первую часть -
2) во вторую часть -
3) в первую часть -
Значит, вероятнее всего, снаряд попал в третью часть цели.
С уважением.
Примем, что для попавшего в цель снаряда вероятность попасть в одну из частей цели пропорциональна площади части.
Сформулируем гипотезы и укажем их вероятности:
1)
- снаряд попал в первую часть. Вероятность равна 2)
- снаряд попал во вторую часть. Вероятность равна 3)
- снаряд попал в третью часть. Вероятность равна По формуле полной вероятности (средняя) вероятность поражения цели (события
) составляетПусть цель поражена. Вычислим условные вероятности попадания снаряда по формуле Байеса (теореме гипотез):
1) в первую часть -
2) во вторую часть -
3) в первую часть -
Значит, вероятнее всего, снаряд попал в третью часть цели.
С уважением.
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
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