Maths 概率

1.
設 P($10) = p，則 P($5)= 3p

P($1) + P($2) + P($5) + P$(10) = 1
(1/3) + (1/5) + 3p + p = 1
4p = (15/15) - (5/15) - (3/15)
4p = 7/15
p = 7/60

抽得一枚 $10 硬幣的概率 = 7/60


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2.
設 P(黑色)=p，則 P(藍色)=(2/3)p 及 P(黃色)=2p

P(白色) + P(灰色)+P(黑色) + P(藍色)+P(黃色) = 1
(3/8) + (1/10) + p + (2/3)p + 2p = 1
(15/40) + (4/40) + (3/3)p + (2/3)p + (6/3)p = (40/40)
(11/3)p = 21/40
p = 63/440
(2/3)p = 21/220

抽出黑色或藍色襯衣的概率
= (63/440) + (21/220)
= 105/440
= 21/88