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Консультация № 198679
23.05.2020, 08:45
0.00 руб.
27.05.2020, 14:30
0
1
1
Здравствуйте! Прошу помощи в следующем вопросе:
В спартакиаде участвуют: из первой группы 11 студентов, из второй – 14. Студент
первой группы попадает в сборную университета с вероятностью 0,9, для студента второй
группы эта вероятность равна 0,7. Найти вероятность того, что выбранный наудачу
студент попадет в сборную университета.
В спартакиаде участвуют: из первой группы 11 студентов, из второй – 14. Студент
первой группы попадает в сборную университета с вероятностью 0,9, для студента второй
группы эта вероятность равна 0,7. Найти вероятность того, что выбранный наудачу
студент попадет в сборную университета.
Обсуждение
27.05.2020, 18:26
общий
это ответ
Здравствуйте, master87!
Если событие А может произойти только при выполнении одного из событий B[sub]1[/sub],...B[sub]n[/sub], которые образуют полную группу несовместных событий (гипотез), то вероятность события А вычисляется по формуле полной вероятности:
где P(A\B[sub]i[/sub]) - условная вероятность наступления события A при выполнении события B[sub]i[/sub].
В данном случае имеем следующие события: A = "студент попадёт в сборную", B[sub]1[/sub] = "студент первой группы", B[sub]2[/sub] = "студент второй группы" (B[sub]1[/sub] и B[sub]2[/sub] несовместны и образуют полную группу событий). Вероятности событий определяем из условий задачи: P(B[sub]1[/sub]) = 11/(11+14) = 0.44, P(B[sub]2[/sub]) = 14/(11+14) = 0.56, P(A\B[sub]1[/sub]) = 0.9, P(A\B[sub]2[/sub]) = 0.7. Тогда по формуле полной вероятности для выбранного наудачу студента вероятность попадания в сборную будет равна
Если событие А может произойти только при выполнении одного из событий B[sub]1[/sub],...B[sub]n[/sub], которые образуют полную группу несовместных событий (гипотез), то вероятность события А вычисляется по формуле полной вероятности:
где P(A\B[sub]i[/sub]) - условная вероятность наступления события A при выполнении события B[sub]i[/sub].
В данном случае имеем следующие события: A = "студент попадёт в сборную", B[sub]1[/sub] = "студент первой группы", B[sub]2[/sub] = "студент второй группы" (B[sub]1[/sub] и B[sub]2[/sub] несовместны и образуют полную группу событий). Вероятности событий определяем из условий задачи: P(B[sub]1[/sub]) = 11/(11+14) = 0.44, P(B[sub]2[/sub]) = 14/(11+14) = 0.56, P(A\B[sub]1[/sub]) = 0.9, P(A\B[sub]2[/sub]) = 0.7. Тогда по формуле полной вероятности для выбранного наудачу студента вероятность попадания в сборную будет равна
5
Спасибо!
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