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Консультация № 199873
15.12.2020, 00:25
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Здравствуйте! У меня возникли сложности с таким вопросом:
Имеются три одинаковых по виду ящика. В первом ящике 6 белых шаров, во втором – 3
белых и 3 черных шаров, в третьем – 6 черных шаров. Из выбранного наугад ящика вынули
белый шар. Вычислить вероятность того, что шар вынут из первого ящика.
Имеются три одинаковых по виду ящика. В первом ящике 6 белых шаров, во втором – 3
белых и 3 черных шаров, в третьем – 6 черных шаров. Из выбранного наугад ящика вынули
белый шар. Вычислить вероятность того, что шар вынут из первого ящика.
Обсуждение
15.12.2020, 07:54
общий
это ответ
Здравствуйте, qazxswedc!
Пусть A - событие, состоящее в том, что взятый шар окажется белым, а H1 и H2 - гипотезы, что он был взят из 1-го и 2-го ящика. (Третий ящик рассматривать не будем, т.к. там только черные шары, а из условий известно, что вынут именно белый шар.)
Вероятности указанных гипотез соответственно равны:
P(H1)=M1/N=6/9=0.67; P(H2)=M2/N=3/9=0.34;
N=6+3=9;
Из условия задачи следует, что:
p1=PH1(A)=6/6=1; p2=PH2(A)=3/6=0.5;
Найдем PA(H1), т.е. вероятность того, что вынутый белый шар был взят из 1-го ящика.
PA(H1)=P(H1)*p1/(P(H1)*p1+(PH2)*p2)=0.67*1/(0.67*1+0.34*0.5)=0.7975
Пусть A - событие, состоящее в том, что взятый шар окажется белым, а H1 и H2 - гипотезы, что он был взят из 1-го и 2-го ящика. (Третий ящик рассматривать не будем, т.к. там только черные шары, а из условий известно, что вынут именно белый шар.)
Вероятности указанных гипотез соответственно равны:
P(H1)=M1/N=6/9=0.67; P(H2)=M2/N=3/9=0.34;
N=6+3=9;
Из условия задачи следует, что:
p1=PH1(A)=6/6=1; p2=PH2(A)=3/6=0.5;
Найдем PA(H1), т.е. вероятность того, что вынутый белый шар был взят из 1-го ящика.
PA(H1)=P(H1)*p1/(P(H1)*p1+(PH2)*p2)=0.67*1/(0.67*1+0.34*0.5)=0.7975
Форма ответа
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