Question

甲、乙兩隊(duì)進(jìn)行一場(chǎng)排球比賽，根據(jù)以往經(jīng)驗(yàn)，單局比賽甲隊(duì)勝乙隊(duì)的概率為0.6.本場(chǎng)比賽采用五局三勝制，即先勝三局的隊(duì)獲勝，比賽結(jié)束.設(shè)各局比賽相互間沒(méi)有影響，求

(1)前三局比賽甲隊(duì)領(lǐng)先的概率；

(2)本場(chǎng)比賽乙隊(duì)以3∶2取勝的概率.(精確到0.001)

Answer 1

解：單局比賽甲隊(duì)勝乙隊(duì)的概率為0.6,乙隊(duì)勝甲隊(duì)的概率為0.4.

(1)記“甲隊(duì)勝三局”為事件A，“甲隊(duì)勝兩局”為事件B，則P(A)=0.6³=0.216,P(B)=×0.6²×0.4=0.432.

所以比賽前3局甲隊(duì)領(lǐng)先的概率為P(A)+P(B)=0.648.

(2)若本場(chǎng)比賽乙隊(duì)3∶2取勝，則前四局雙方應(yīng)以2∶2戰(zhàn)平且第五局乙隊(duì)勝.

∴所求事件的概率為×0.4²×0.6²×0.4=0.138.