Question

Will fan and medal!!!!

A bag contains 5 red beads, 2 green beads, and 3 yellow beads.
A.) What is the probability that 2 beads drawn at random (with replacement) are yellow?
B.) What is the probability that 2 beads drawn at random (with replacement) are not yellow?

Answer 1

The first step to solving most probability questions is to work out the "sample space", that is, the total number of things that can happen. Usually, you just have to add up the number of items you have, so for this scenario, we would add 5 + 2 + 3 = 8.
Another thing to keep in mind with probability is that AND = X (multiplication) and OR = + (addition).

A.) Let's break this down into two things that happen. First, we want the probability that we draw a yellow. There are 3 yellows out of a total of 8, so that's 3/8. Now we put that yellow bead back so the total number of beads is still 8 (that's what replacement means!).
Now we want to draw a yellow again, so it would be 3/8 again. We want to draw yellow AND yellow, so we multiply the probabilities together.

B.) We can use part A to work this out - it's the same question, but the probability that the previous scenario doesn't happen. That's called a "complementary event", and to work it out, we just do 1 minus the other probability, because 1 = 100% and the probability of two complementary events has to add up to 100%.
For example, the chance of flipping a heads is 1/2, and the chance of flipping a tails is also 1/2. 1/2 + 1/2 = 1.

Hope that helps you figure it all out.

Answer 2

@Tommynaut so if I understand correctly, you're saying the answer to A would be 3/8 * 3/8 which is 9/64? :)

Answer 3

Yep!

Answer 4

@Tommynaut then that would make B 55/64. Thank you so much for your help! You broke it down perfectly for me :)

Answer 5

No problem, super glad I could help you understand it :)