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Math / Statistics / Grade 7 / mt7p2

Compare Tile Chances

Compare fractions and explain why a likely result is not guaranteed.

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Count equally likely individual tiles, then divide the wanted count by the whole bag count. Compare proportions rather than wanted counts alone. The chance of either of two non-overlapping shapes uses their combined count. The chance rule describes possible draws; it does not require a short sequence to match that fraction exactly. Each question states its own model.

Worked example

Bag X has 1 star in 4 tiles, while Bag Y has 2 stars in 8 tiles. Both give a star chance of 1/4, since 2/8 = 1/4. Doubling every category preserves the chance. Doubling only the star count would change the mix.

Bag B contains two labeled stars, one labeled triangle and three labeled circles. Each individual tile is equally likely.
Use Bag B for Questions 1 and 2. S means star, T triangle and C circle.
Question 1 Bag B has 2 stars, 1 triangle and 3 circles. What is the chance of drawing a triangle?
Question 2 Using Bag B, what is the chance of drawing a star OR a triangle? Each tile has just one shape.
Question 3 Bag X has 2 stars and 6 circles. Bag Y has 3 stars and 9 circles. Which has the greater star chance?
Question 4 A bag has 1 star and 1 circle. A tile is returned after each draw. Must ten draws contain exactly five stars?
Question 5 A device chooses between a star tile and a circle tile, but it may favor one tile. Can two tile names alone prove a 1/2 star chance?