math- drawing two even numbers

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joonkimdds

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Two numbers between 1 and 30 inclusive are drawn in a contest. What is the probability that both numbers are even?

I believe there are 15 even and 15 odd numbers.
The chance of first card being even is 15/30
The chance of second card being even is 14/29
so i think we should multiply these two numbers and I get 7/29.

But the solution says
15/30 x 15/30 = 1/4.

Am I wrong?



Another question I have is...
if it says how many numbers are there between 0 to 10,
do we include both 0 and 10 thus total of 11 numbers or
do we just count 1~9 without including 0 and 10?

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It depends how the question is worded. In the first question you asked it said numbers between 1-30 "INCLUSIVE". Look for key words like that.
 
It depends how the question is worded. In the first question you asked it said numbers between 1-30 "INCLUSIVE". Look for key words like that.

yeah, when it says inclusive, i understand, but I saw many other questions that didn't specify like that.

Anyway, do you know about the first question that I asked?
 
It depends how the question is worded. In the first question you asked it said numbers between 1-30 "INCLUSIVE". Look for key words like that.
so when they say the word "inclusive" we can use the number more than one?
 
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so when they say the word "inclusive" we can use the number more than one?

No, when it says inclusive it means
"inclusive refers to the set {-2,-1,0,1,2}; the endpoints, -2 and 2, are included"
says wikipedia.

it just means "between 0 to 10" includes 0 and 10, not just 1~9.

but now my real question is,
1. why does 15 stay 15 even after one card is already picked?
shouldn't it become from 15 to 14?

2. if it doesn't say inclusive, does that mean it's automatically inclusive or exclusive?
 
No, when it says inclusive it means
"inclusive refers to the set {-2,-1,0,1,2}; the endpoints, -2 and 2, are included"
says wikipedia.

it just means "between 0 to 10" includes 0 and 10, not just 1~9.

but now my real question is,
1. why does 15 stay 15 even after one card is already picked?
shouldn't it become from 15 to 14?

2. if it doesn't say inclusive, does that mean it's automatically inclusive or exclusive?

1) All I can say is that the question is unclear, it should say "with replacement" to have 15/30 x 15/30 and "without replacement" to have 15/30 x 14/29.

2) this again is unclear. but imo, it should be automatically inclusive.
 
1) All I can say is that the question is unclear, it should say "with replacement" to have 15/30 x 15/30 and "without replacement" to have 15/30 x 14/29.

2) this again is unclear. but imo, it should be automatically inclusive.

for question 1, if it's doesn't say w/ or w/out replacement, should it automatically be w/ replacement?
 
for question 1, if it's doesn't say w/ or w/out replacement, should it automatically be w/ replacement?

NO, you can never know, a question like this isn't fair, don't worry about it, as long as you know how to do it both ways then your set.
It is like me saying my favorite color is blue then someone assuming it is light blue...what a great analogy.
 
I would do 15 x 14 also. Since it's a contest I would assume that there's no replacement when you draw two numbers for the same thing. Normally I'd assume no replacement in these problems unless stated or implied. If they were drawing 2 numbers for 2 separate raffles then one may assume that there will be replacement for example.

Hopefully they don't have both answer choices.
 
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