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Math / Statistics / Grade 7 / mt7u2

At Least One or Exactly One: Keep Tiles Out

Exclude impossible repeats before comparing two event definitions.

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Explore these events in Chance Lab

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Each named tile is a physical object. Keeping the first tile out removes that same object from the second choices. Exclude same-name pairs, but keep both orders of different tiles. At least one star includes one or two stars; exactly one excludes two stars. These events can have equal chances when two stars are impossible. Reset the bag for each question.

Worked example

A worked bag has S1, C1 and C2. Keep the first tile out. There are 3 x 2 = 6 allowed paths. Four have exactly one star; two have zero stars. There is only one physical star, so no allowed pair has two stars. At least one and exactly one both have chance 4/6 here. They are not always equal.

Worked example only: S1, C1, C2. Keep the first tile out; same-name pairs are impossible. 6 allowed paths. Exactly one: 4/6. At least one: 4/6. Two stars: impossible. Rows name the first tile, columns the second. Each cell names its star count.
Worked example only. The questions use their own bags and return rules.
Question 1 A NEW bag has 2 stars and 3 circles, each equally likely. Draw twice, keeping the first tile out. What is the chance of AT LEAST ONE star?
Question 2 Use 2 stars and 3 circles, keeping the first tile out. What is the chance of EXACTLY ONE star?
Question 3 Use that same bag. How many allowed ordered pairs have TWO stars when the first tile stays out?
Question 4 A different bag has 1 star and 3 circles. Keep the first tile out. What is the chance of at least one star in two draws?
Question 5 A NEW bag contains 4 stars and no circles. Keep the first tile out. Compare at least one star with exactly one star in two draws.