probability?

用戶40441

2016-11-01 12:14 pm

In a game, someone first randomly picks a sequence of 4 pegs from 6 pegs of different colours. A player then tries to guess the exact positions of the 4 coloured pegs in the sequence.
a) Find the probability that the player guesses
i) the colours of the 4 pegs correctly.
ii) the exact positions of the 4 pegs correctly given that the player guessed the colours of the 4 pegs correctly.

更新1:

師兄,可否加少少中文解釋，我怕我睇唔明?

回答 (1)

2016-11-01 5:43 pm

✔ 最佳答案

ai. 4/6 * 3/5 * 2/4 * 1/3 = 1/15

First, you guess one colour from 6 choices. There are 4 correct answer so P(correct) = 4/6. Now there are 5 pigs left and you still need to guess 3 colours. P(correct) = 3/5. 如此類推...

aii. This is conditional probability. The probability should be P(條件A AND 條件B) / P(條件B), where B is the given situation.
B is the same as Qs ai so
P(條件B) =ans from ai.

P(條件A AND 條件B) means you need to get both ORDER and COLOUR correct.
豬因為顏色不同, 所以有分次序, which means order matters. Therefore use P. Selecting 4 from 6, so total permutation = 6P4. Since the colours are unique, therefore when you guess, you only have one choice. For example, the correct order is Red > Blue > Yellow > Green. Then the correct guess can only be Red > Blue > Yellow > Green. Therefore numerator is 1.

So ans shd be 1/(6P4) / (1/15) = 1/24

I am sorry I can't type Chinese.

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