Imagine you have a bag with 3 red marbles and 2 blue marbles. That’s 5 marbles in total. You draw two marbles, but after you take the first one out, you put it back before drawing again. This is called drawing with replacement.

Step 1: Chance of getting a red marble

• There are 3 red marbles out of 5 total:

• P(red) = 3/5 = 0.6

Step 2: Chance of getting a blue marble

• There are 2 blue marbles out of 5 total:

• P(blue) = 2/5 = 0.4

Step 3: What happens when you replace the marble?

• After the first draw, you put the marble back — so the bag still has 3 red and 2 blue marbles.

• That means the probabilities stay the same for the second draw.

Step 4: Example — Getting red then blue

• First draw: P(red) = 3/5

• Second draw: P(blue) = 2/5

• Because you replaced the first marble, multiply them:

• P(red then blue) = (3/5) × (2/5) = 6/25 ≈ 0.24

• That’s about a 24% chance.

Step 5: Why multiply?

• With replacement, each draw is independent — what happens first doesn’t affect the second.

• So, to find the probability of both happening, you multiply them together.

Tip:

• “With replacement” → multiply.

• “Without replacement” → the second probability changes.