Question

某次測(cè)驗(yàn)有10道備用試題，甲同學(xué)在這10道題中能夠答對(duì)6題，現(xiàn)在備用試題中隨機(jī)抽考5題，規(guī)定答對(duì)4題或5題為優(yōu)秀，答對(duì)3題為合格．求甲同學(xué)獲優(yōu)秀的概率．

Answer 1

因?yàn)榧淄瑢W(xué)在這10道備用試題中能夠答對(duì)6題，
可以知道甲同學(xué)答對(duì)題目的概率是P=

3

5

，答不對(duì)題目的概率是p=

2

5

．
當(dāng)甲同學(xué)在5題中答對(duì)4題，p1=

3

5

×

3

5

×

3

5

×

3

5

×

2

5

當(dāng)甲同學(xué)全答對(duì)5題，有p2=

3

5

×

3

5

×

3

5

×

3

5

×

3

5

所以，甲同學(xué)獲優(yōu)秀的概率p1+p2 =

81

625

故答案為

81

625

．