maths <

2008-06-11 7:36 pm
1. There are 9 cards with numbers 1 to 9 marked on them respectively. If 2
cards are drawn at random, what is the probability that the product(積) of
the numbers is even?
個答案係: 13/18
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回答 (2)

2008-06-11 8:21 pm
✔ 最佳答案
Method a.)
Since as long as 1 of the 2 cards is even, then the product of 2 cards must even

Step 1: Find the total possible outcome.
Since 2 cards are drawn from 9, so, there have 9^2;
then minus the same number of cards(which is impossible to exits at the same time), that is 9
Thus, total possible outcome is 9^2 - 9 = 72

Step 2: Count the even product.
If the fisrt is odd, the even product outcome
= 5 odd number at first (1, 3, 5, 7 and 9) * 4 even number at second (2, 4, 6 and 8)
= 5*4
=20
If the fisrt is even, the even product outcome
= 4 even number at first (2, 4, 6 and 8) * 8 number at second (any number except the number in fisrt draw)
= 4*8
= 32
Total Even outcome = 52
Hence the probabity of even product = 52/ 72 = 13/18




Method b.)
The product will be odd only if both cards are odd
First draw is odd = 5/9
Second draw is odd = 4/8
So, probability of the odd product = 20/72
Hence, probability of the odd product = 52/72 =13/18
2008-06-11 8:07 pm
有9張CARDS咁就有81個可能,但係without replacement,姐係無減9個可能,一共得72個可能

evenX even= even
odd X even= even
evenX odd= even
odd Xodd = odd

1至9有5個單數,so that全部有25個可能,但係without replacement,姐係無減5個可能,一共得20個可能

1- the product of the numbers is odd
=the product of the numbers is even
=1-20/72
=52/72
=13/18
參考: 自己!


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