Track Two Draws Without Replacement

Supplied materials

• Paper or a note app.
• Fictional uniform box: 3 red cards and 2 blue cards. Draw two cards in order without replacing the first.

Learn the idea

Without replacement, the first card is absent during the second draw. For red then blue, the first red probability is 3/5. After that red draw, four cards remain and two are blue, so the next blue probability is 2/4.

Multiply along this specified path: P(red then blue) = P(red first) × P(blue second given red first). This is a conditional multiplication rule. You cannot keep the original denominator five for the second draw. Replacement would produce a different model.

1. Write the starting counts as 3 red, 2 blue, total 5.
2. On the red-first branch, update to 2 red, 2 blue, total 4.
3. Multiply 3/5 by 2/4, then update both counts for the new two-red question.

Check your reasoning

Your answer is temporary and is not saved to an account. Download your current answer before leaving or reloading. Written work on paper or in another app stays in your own file.

Take it further

Replace the first card before the second draw in that 4-red, 2-blue box. Both red now has probability (4/6)(4/6) = 4/9, because the second sample space is reset.

Nothing here is saved to an account or sent to a teacher. The answer download includes your current choice and any checked feedback.