S3U

Math / Statistics / Grade 7 / mt7t2

Count Two-Draw Paths without Returns

Remove impossible same-tile paths and explain the difference between a known first draw and a whole pair.

All worksheets

Watch the lesson | Explore two-draw paths in Chance Lab

5 questions0m 0s
Learn the skill

Name every individual tile. When the first tile stays out, that same physical tile cannot be drawn again, but a different tile of the same shape may remain. List first-then-second paths and exclude only the impossible ones. All allowed paths in this uniform two-draw model are equally likely. A probability for two stars together is not the probability of a second star GIVEN that the first was a star. Reset between questions.

Worked example

A separate worked bag has S1, S2, S3 and C1. Keep the first tile out. Each of 4 first choices leaves 3 second choices: 12 equally likely paths. The 3 stars each have 2 other stars that can follow, so 6/12 = 1/2 of all pairs have two stars. Same-name pairs such as S2 then S2 are excluded, not all same-shape pairs.

Worked bag S1, S2, S3, C1 without returns. A four-by-four grid excludes four same-name cells. Six of the twelve allowed ordered pairs contain two different star tiles.
Worked example only: three stars and one circle. The questions use two stars and one circle.
Question 1 A NEW bag has S1, S2 and C1. Each remaining tile is equally likely. Draw twice, keeping the first tile out. How many equally likely ordered pairs are possible?
Question 2 Use S1, S2, C1 without returns. What is the chance of TWO stars?
Question 3 Use S1, S2, C1 without returns. What is the chance of EXACTLY ONE star, in either order?
Question 4 Use S1, S2, C1 without returns. What is the chance of TWO circles?
Question 5 Reset to S1, S2, C1 without returns. This time we are TOLD the first tile was S1. What is the chance that the NEXT tile is a star?