CPM Homework Help : MC2 Problem 3-86

Troy has a number cube with the numbers $1$ through $6$ on it. Assuming each side is equally likely to appear when he rolls the cube, find the following probabilities. Note: When two or more numbers are multiplied, each of the numbers is a factor of the product.

Hint:

Remember that the probability of any event is:

$\large\frac{\text{Number of successes}}{\text{Total number of outcomes}}$

P(rolls a $2$ )
Hint (a):
There is only one way to roll a $2$ and there are six possible outcomes on any given roll.
Knowing this, can you write the probability of rolling a $2$ ?

P(rolls an odd number)
Hint (b):
How many odd numbers are there from $1$ to $6$ ?

P(rolls a factor of $6$ )
Answer (c):
There are four factors of $6$ : $1$ , $2$ , $3$ , and $6$ .
That means there are four possible successes.
Thus, the probability of rolling a factor of $6$ is $\frac{4}{6}$ or $\frac{2}{3}$ .