Question

A jar contains 6 aqua beads and 4 black beads. If two beads are selected at random, what is the probability that both beads will be aqua? Round to the nearest hundredth if needed.

Answer 1

0.33

Explanation:

We would like to find the probability that both beads are aqua.

There are 6 aqua beads. Let's calculate the number of ways we can select 2 aqua beads from these 6. We use combinations, which is
`_6C_2=(6!)/((6-2)!*2!)`, where the n! means n * (n - 1) * (n - 2) * ... * 2 * 1.

The value of the expression is:

`_6C_2=(6!)/((6-2)!*2!)=(720)/(24*2) =15`

So there are 15 ways to choose 2 aqua beads.

Now let's calculate the number of ways we can select any 2 beads. There are 6 + 4 = 10 beads in total, so we do the same thing as before using combinations:

`_(10)C_2=(10!)/((10-2)!*2!) =(3628800)/(40320*2) =45`

Our fraction is thus:

15 / 45 = 1/3 ≈ 0.33

The answer is thus 0.33.

~ an aesthetics lover