Question

A die is rolled. What is the probability of Rolling a 6 or a number higher than 4

Answer 1

This is a standard 6-sided die, numbered 1,2,3,4,5,6?

How many ways are there to roll a number higher than 4? How many ways are there to roll a 6? Are any of those ways the same way?

Answer 2

We want to count all of the possible ways that we can get the outcome we want. We'll divide that number by all of the different possible outcomes. The quotient will be our probability.

As an example: what is the probability of rolling a 1 or a 2? Well, there's 1 way to roll a 1, and 1 way to roll a 2, and they are separate, so that means there are 2 outcomes that we want. How many different outcomes are there in all? Well, the die has 6 sides, so there are 6 possible outcomes. Our probability of rolling a 1 or a 2 is therefore \[P = \frac{2}{6} = \frac{1}{3}\approx 0.3333\]

Answer 3

5 and 6 are gerater than 4 so 2/6 or 1/3

Answer 4

@courtneyconaway

Answer 5

Oh... I accept medals as well as fans

Answer 6

A key point here is that we don't want to double-count 6 as two ways to get our desired outcome: it's not
\[P = \frac{2+1}{6} = \frac{3}{6} = \frac{1}{2}\](thinking "2 rolls are larger than 4, and you can roll a 6 1 way")
but \[P = \frac{2}{6}=\frac{1}{3}\]

Answer 7

Now if we had a slightly different problem: what is the probability of rolling either a number > 4 OR rolling a 1, then it would be
\[P = \frac{2+1}{6} = \frac{1}{2}\]because the outcome of rolling a 1 is separate from the 2 outcomes of rolling a number > 4. Do you see the difference?

Answer 8

@whpalmer4 yes I didn't see it