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.
分析:首先分析題目要求甲同學(xué)獲優(yōu)秀的概率,則可分兩種情況:當(dāng)甲同學(xué)在5題答中對(duì)4題和當(dāng)甲同學(xué)全答對(duì)5題.然后分別求出概率,相加即可得到答案.
解答:解: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=
,答不對(duì)題目的概率是p=
.
當(dāng)甲同學(xué)在5題中答對(duì)4題,
p1=××××當(dāng)甲同學(xué)全答對(duì)5題,有
p2=××××所以,甲同學(xué)獲優(yōu)秀的概率
p1+p2 =故答案為
.
點(diǎn)評(píng):此題主要考查概率問(wèn)題的求法,在做此類(lèi)題目的時(shí)候要仔細(xì)分析題目,抓住重點(diǎn)條件才能很好的做題.屬于基礎(chǔ)題目.