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

Answer:

0.33

Step-by-step 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 $_6C_2=\frac{6!}{(6-2)!*2!}$, where the n! means n * (n - 1) * (n - 2) * ... * 2 * 1.

The value of the expression is:

$_6C_2=\frac{6!}{(6-2)!*2!}=\frac{720}{24*2} =15$

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:

$_{10}C_2=\frac{10!}{(10-2)!*2!} =\frac{3628800}{40320*2} =45$

Our fraction is thus:

15 / 45 = 1/3 ≈ 0.33

The answer is thus 0.33.

~ an aesthetics lover