2001 CEMC Gauss (Grade 8) Problems/Problem 8

The following problem is from both the 2001 CEMC Gauss (Grade 8) #8 and 2001 CEMC Gauss (Grade 7) #11, so both problems redirect to this page.

Problem

A fair die is constructed by labelling the faces of a wooden cube with the numbers $1\text{, } 1\text{, } 1\text{, } 2\text{, } 3\text{, and } 3$

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$\text{ (A) }\ \frac{5}{6} \qquad\text{ (B) }\ \frac{4}{6} \qquad\text{ (C) }\ \frac{3}{6} \qquad\text{ (D) }\ \frac{2}{6} \qquad\text{ (E) }\ \frac{1}{6}$

Solution 1

We can find how many times an odd number appears and divide it by the total number of sides on the die, as every number is equally likely.

There are $6$ numbers in total, and $5$ of them are odd. Thus, the probability that the number rolled is odd is $\boxed {\textbf {(A) } \frac{5}{6}}$ .

~anabel.disher

Solution 2

Since all of the numbers are integers, we can find the probability that we get an even and subtract it from $1$ .

There are $6$ numbers in total, and $2$ is the only even number, with $1$ occurrence. Thus, the probability that the number rolled is even is $\frac{1}{6}$ .

Subtracting this from $1$ to find the probability of rolling an odd, we get:

$1 - \frac{1}{6} = \frac{6}{6} - \frac{1}{6} = \frac{6 - 1}{6}$

$=\boxed {\textbf {(A) } \frac{5}{6}}$

~anabel.disher

2001 CEMC Gauss (Grade 8) (Problems • Answer Key • Resources)
Preceded by Problem 7	Followed by Problem 9
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CEMC Gauss (Grade 8)

2001 CEMC Gauss (Grade 7) (Problems • Answer Key • Resources)
Preceded by Problem 10	Followed by Problem 12
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CEMC Gauss (Grade 7)

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2001 CEMC Gauss (Grade 8) Problems/Problem 8

Problem

Solution 1

Solution 2