Find the probability for the experiment of drawing two marbles at random (without replacement) from a bag containing four green, two yellow, and two red marbles.

Answer 1

Hey! Two key things to finding simple probability (with or without replacement). Let's say we're given an event E, indicating something has happened.

1. The first thing is knowing that P(E) = (desired outcome)/ (total # of outcomes).

The total # of outcomes (also called the sample space) will stay the same with replacement. This is because you're putting the chosen event back into the original space!

HOWEVER, without replacing the event, the total number of outcomes will change! It will ALWAYS decrease too. Say if you drew one card from a deck without replacing. (Then the sample space would decrease from 52 to 51).

1. The second thing is knowing that for independent events (like coin flips, card draws, ball draws, etc.), we have. P(E₁) x P(E₂).

In this example, I'm assuming we want to know the probability of drawing one ball after the other. Since we can draw any ball (and we don't care about the color), we have...

P(E₁) = 1/8

P(E₂) = 1/7

Hope this helps!