Probability

👨🏻‍🏫 學術台數學

[匿名]

2011-06-15 2:17 am

3 balls are to be drawn from a bag with 5 red balls, 4 blue balls and 1 black balls. What is the probability of :
(a) Draw at least 1 red ball.
(b) Draw 2 red balls.
(c) Draw at least 1 red ball AND 2 red balls.

更新1:

Note : It is without replacement.

更新2:

To : Yiu Man. Please explain why the answer of (c) 137/144 is greater than (a) 11/12 = 132/144.

回答 (2)

Yiu Man

2011-06-15 5:36 am

✔ 最佳答案

(a) 1-5/10*4/9*3/8 = 11/12
(b) 5/10*4/9*5/8+5/10*5/9*4/8+5/10*5/9*4/8 = 5/12
p.s:(有3個cases,分別係第1同第2次都抽到紅波, 第1次同第3次抽到紅波, 同埋第2次同第3次先抽到紅波)
(c) 11/12+5/12-(11/12*5/12) = 137/144
(因為at least 1 red ball 包含左2 red balls既possibility, 所以要減去a*b既答案)

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知識就是力量

2011-06-15 2:28 am

With replacement or without replacement?

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