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Math / Statistics / Grade 7 / mt7u1

At Least One or Exactly One: With Returns

Read the event carefully before counting equally likely two-draw paths.

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Name each physical tile, even when shapes match. Count first tile then second tile. Return the first tile before the second draw. At least one star includes one-star and two-star pairs. Exactly one includes only mixed pairs, in either order. Zero or two stars is the opposite of exactly one. Reset the stated bag for each question.

Worked example

A worked bag has S1, C1 and C2. With returns there are 3 x 3 = 9 paths. Four have exactly one star, one has two stars and four have zero stars. At least one star has 4 + 1 = 5 paths, giving 5/9; exactly one has 4/9. S1 then S1 belongs only to at least one. The questions use different bags.

Worked example only: S1, C1, C2. Return the first tile. 9 equally likely paths. Exactly one: 4/9. At least one: (4 + 1)/9. Zero stars: 4/9. 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, returning the first tile. What is the chance of AT LEAST ONE star?
Question 2 Use 2 stars and 3 circles with returns. What is the chance of EXACTLY ONE star?
Question 3 For two draws, what is the opposite event to EXACTLY ONE star?
Question 4 A different bag has 1 star and 3 circles. Return the first tile. What is the chance of at least one star in two draws?
Question 5 A two-star pair is observed from the 2-star, 3-circle returned bag. Does that make at least one star certain on the next fresh pair?