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Algebra 2 9-12 / Week 11 / Garden Day
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Week 11 · Probability in the Seed Trays

Garden Day

Garden Day: the sock drawer table
// Sprouted or not, misted or not
⏱ about 20 min

Garden Day: The Sock Drawer Table

Saturday the sock drawer is emptied onto the bed, and the family sorts.

"Two questions," Comet says. "Striped or plain. Long or short. Every sock lands in one box."

They count. 5 striped and long. 7 striped and short. 9 plain and long. 3 plain and short.

"Now the questions," Wren says. "Pick a sock with your eyes shut. What are the chances it is long?"

"7/12," someone answers after a moment. "And given that it is striped?"

"5/12," Comet says. "Lower. In this drawer, stripes and length are linked. What do you notice?"

Nova hovers over the piles. "Would you like a hint? Try the product test before you decide."

  1. A two-way table is the sample space. Every object lands in exactly one box.
  2. Events are sets of boxes: a row, a column, an "and" box, an "or" union, a "not" complement.
  3. P(A given B) = cells in both ÷ cells in B = P(A and B) ÷ P(B). Order matters.
  4. Independent means P(A given B) = P(A), the same as P(A and B) = P(A) × P(B).
  5. P(A or B) = P(A) + P(B) - P(A and B): the overlap is counted once.
◇ FAMILY TWO-WAY TABLE
Pick a drawer, a shelf or a toy box. Choose two yes-or-no questions about the objects in it.
Sort every object into a two-row, two-column table. Write the row, column and grand totals.
Take turns asking: P(a row), P(a column), P(one given the other). Say each answer in everyday words.
Run the product test together. Are your two questions independent in this drawer?
For a grown-up
Choose objects that are safe to handle and sort on a table or bed. Nothing is climbed for.
A disagreement about a count is a good moment: recount together and fix the table.
The numbers belong to your drawer only, like the crew's trays. No fact about socks in general is being claimed.
GARDEN DAY CHECK
  • Read the question.
  • Tap your answer.
A two-way table: rows Striped and Plain, columns Long and Short, counts 5 and 7; 9 and 3, total 24.One sock is picked at random from the 24. What is the probability it is long?
A two-way table: rows Striped and Plain, columns Long and Short, counts 5 and 7; 9 and 3, total 24.Given that the sock is striped, what is the probability it is long?
P(Long) = 7/12 and P(Long given Striped) = 5/12. Are "Long" and "Striped" independent?
How many socks are striped and long? Type the number.
WHY THIS EXERCISEThat box is the top of P(long given striped) and of P(striped given long). Every "given" starts there.
Draw your family two-way table with totals. Shade the box you used for your favorite "given that" question.
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