A `CONTAINER` contains

red `REDMAR``MARBLE`s,

green `GREENMAR``MARBLE`s, and

blue `BLUEMAR``MARBLE`s.

If a `MARBLE` is randomly chosen, what is the probability
that it is *not* `CHOSEN_COLOR`? Write your answer as a simplified fraction.

There are `REDMAR` + `GREENMAR` + `BLUEMAR` = `TOTAL``MARBLE`s in the `CONTAINER`.

There are `CHOSEN_NUMBER``CHOSEN_COLOR` `MARBLE`s.
That means

are `TOTAL` - `CHOSEN_NUMBER` = `NUMBER`*not* `CHOSEN_COLOR`.

The probability is `\displaystyle `

.`fractionSimplification(NUMBER, TOTAL)`

A fair six-sided die is rolled. What is the probability that the
result is `RESULT_DESC`? Write your answer as a simplified fraction.

When rolling a die, there are `6`

possibilities: 1, 2, 3, 4, 5, and 6.

In this case, only `1`

result is favorable: the number `RESULT_POSSIBLE[0]`.

In this case,

results are favorable: `RESULT_COUNT``toSentence(RESULT_POSSIBLE)`.

The probability is `\displaystyle `

.`fractionSimplification(RESULT_COUNT, 6)`

You throw a dart at a circular dartboard with `BIG_GIVEN` `BIG_INFO`

. Inside the dartboard is a circular target with
`BIG_GIVEN === "circumference" ? "\\pi" : ""``SMALL_GIVEN` `SMALL_INFO`

.
Assume you're good enough to hit the dartboard every time, and you'll hit every point on the dartboard with equal probability.
`SMALL_GIVEN === "circumference" ? "\\pi" : ""`

What is the probability that you will hit the target?

Since you're equally likely to hit every point on the dartboard, the probability that you hit the target is basically the size of the target divided by the size of the dartboard.

To figure out these sizes, we need to figure out the areas of the target and the dartboard.

The area of the dartboard is `\pi r^2`

, so since

,
the area of the dartboard is `BIG_GIVEN === "radius" ? "radius =" + BIG_INFO :
(BIG_GIVEN === "diameter" ? "radius = \\frac{diameter}{2}" : "radius = \\frac{circumference}{2 \\pi}")`

.
`BIG_RAD`^2 \pi

The area of the target is `\pi r^2`

, so since

,
the area of the target is `SMALL_GIVEN === "radius" ? "radius =" + SMALL_INFO :
(SMALL_GIVEN === "diameter" ? "radius = \\frac{diameter}{2}" : "radius = \\frac{circumference}{2 \\pi}")`

.
`SMALL_RAD`^2 \pi

So, the probability that you will hit the target is ` \frac{`

.
`Math.pow(SMALL_RAD,2)`}{`Math.pow(BIG_RAD,2)`}
= \frac{`Math.pow(SMALL_RAD,2)/GCD`}{`Math.pow(BIG_RAD,2)/GCD`}

So, the probability that you will hit the target is ` \frac{`

.
`Math.pow(SMALL_RAD,2)`}{`Math.pow(BIG_RAD,2)`}