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Math / Statistics / Grade 7 / mt7r1

Return a Tile or Keep It Out

Recount the remaining bag after a stated result, before predicting the next draw.

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Every remaining individual tile is equally likely on the next draw. Returning a drawn tile restores the original counts. Keeping it out removes one tile from the total and, if it matches the wanted shape, one from the wanted count too. Do not multiply probabilities here: the earlier draw is already given. Each question resets the bag unless it explicitly describes a sequence.

Worked example

A separate bag starts with 4 stars and 2 circles. After a circle is drawn and kept out, 4 stars and 1 circle remain: next star chance 4/5. If that circle is returned instead, the next star chance is back to 4/6. Count what is available now.

Starting bag: three stars and two circles. After one star is kept out: two stars and two circles remain. After that star is returned instead: three stars and two circles remain.
The two lower rows are alternatives starting from the same original bag, not successive actions.
Question 1 Start with 3 stars and 2 circles. A star is drawn and KEPT OUT. What is the next star chance?
Question 2 Reset to 3 stars and 2 circles. A star is drawn and RETURNED. What is the next star chance?
Question 3 Reset to 3 stars and 2 circles. A circle is drawn and KEPT OUT. What is the next star chance?
Question 4 Reset to 3 stars and 2 circles. One star and then one circle are drawn, both KEPT OUT. What is the next star chance?
Question 5 A different bag starts with 1 star and 1 circle. Three stars were drawn in a row, each returned. What is the next star chance?