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Let there be a nonperfect die with the numbers $1$ to $6$ on its faces. It's known that all even numbers have the same probability to face up and the all odd numbers have the same probability either. It's also known that the chance to get a prime number is $0.4$.

What is the probability of getting the number $1$?

As I understood, we can not apply to the Laplace rule, because the elementary events don't have the same probability. However in the sample set of this experience, one have $3$ odd numbers that happen to be also prime numbers ($1,3$ and $5$).

So I thought that being a odd number imply to be a prime number. In this way the probability to get a prime number is the same of getting an odd number. And by the text we know that each odd number have the same chance to face up.

But now I can't figure it out how to find the probability of gettin a given odd number. Can you help me?

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Note: $1$ is not a prime (according to the modern meaning of that word). But $2$ is. –  Henning Makholm Mar 21 '12 at 19:46
    
The singular of "dice" is "die". By the way, do you disapprove of spacing after punctuation? :-) –  joriki Mar 21 '12 at 19:58
    
It's ok by me. Thanks to correct my english –  João Mar 21 '12 at 20:32
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1 Answer

up vote 5 down vote accepted

Let $a$ be the probability of getting any specific odd number, and let $b$ the probability of getting any specific even number. Then $3a+3b=1$.

The probability of a prime ($2$ or $3$ or $5$) is $0.4$. But this is $2a+b$. Now we have two equations in two unknowns. Solve for $a$ (and, if you wish, $b$).

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I chosen this answer, because presents a solution that make use of a different area of mathematic.I didn't even thought to apply algebra to solve the problem.Thanks –  João Mar 21 '12 at 20:44
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