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Episode 4 · Stories from Ganita House

Marbles in the Bag

ChanceTally charts

Anna brings out a cloth bag for a guessing game, but Chitra will not guess blind. First the bag is loaded and counted in front of everyone: six red marbles, three blue and one yellow. Then ten picks test what 'most likely' really means.

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Read the story

The same story, told as a comic. Read it together, slowly.

The Ganita house, with its wooden name board1
In a big, happy house called Ganita, there lived a girl who loved numbers. Her name was Chitra.
Anna holding up the cloth bag on the veranda, with Chitra and Shruthi at the table2
Anna had a game, and a cloth bag to play it with. But Chitra set the terms first.
AnnaA guessing game! I shake the bag, you pick, and you guess the colour before it comes out.
ChitraNo guessing blind, Anna. First we count what goes into the bag.
ShruthiAnd I write everything down. Then the game has proof.
AnnaRules first, then. Load the bag, counters!
The tray before loading: six red marbles, three blue and one yellow, beside the open bag3
So the bag was loaded on the table, one marble at a time, counted out loud as each one went in.
ChitraReds first. One, two, three, four, five, six.
ShruthiBlues. One, two, three.
AnnaAnd the yellow. One. Just one in the whole bag.
The empty tray and the tied bag, with all ten marbles inside4
With the bag tied and shaken, Chitra made one careful claim, from the counts alone.
ChitraTen marbles in the bag: six red, three blue, one yellow.
ChitraSo pick without looking, and red is the most likely. Six of the ten are red.
ShruthiMost likely, Anna. Likely is not promised.
AnnaThen we test it. Ten picks! And I keep the score.
Chitra answering Anna's question, with Shruthi's chart showing four red and one blue after five picks5
Every pick was named, tallied by Shruthi, put back in and shaken before the next. The first five picks ran red, blue, red, red, red: three reds in a row.
AnnaThree in a row. Does that make blue due next, Chitra?
ChitraThe bag does not remember, Anna. Every pick, it is the same six, three and one.
Pick seven: the only yellow marble in the bag, on the tray6
Back in went every marble. Shake, and pick again. Blue came at pick six, not because it was due, but because it was in there.
ShruthiBlue came. Not because it was due. Because it was in there.
ChitraPick seven. Yellow! The only one in the bag!
Shruthi's finished tally chart: red six, blue three, yellow one7
After pick ten, Shruthi read the chart. It is the record of the whole game, written down pick by pick.
ShruthiTen picks, all written down. Red six. Blue three. Yellow one.
AnnaSix, three and one. Just like the bag itself!
ChitraThis time it landed like the bag. Chance never promises that. It only says what is likely.
Anna, Chitra and Shruthi at the table at the end of the game, the finished chart beside them8
And Anna was already planning the next game.
AnnaNext time, two more blues go in!
ChitraFive blue against six red then. Still red in front, but a much closer race.
ChitraProven.

Try the math

Pick from the bag, then tally

0 of 10 picks · Red 0 · Blue 0 · Yellow 0

In the bag, every pick: 6 red, 3 blue, 1 yellow. Every marble goes back in, so the bag never changes.

On the tray

The tray is empty. Pick a marble to begin.

Shruthi's tally chart

RED

none yet

0

BLUE

none yet

0

YELLOW

none yet

0

Your Turn

Next time, Anna puts two more blue marbles in, so the bag holds 6 red, 5 blue and 1 yellow. Red is still the most likely pick. If they play ten picks again, will red surely come out most?

Off-screen activity

At home: put 6 red, 3 blue and 1 yellow button, crayon or counter in a bag. Take turns: pick without looking, say the colour, tally it, put it back and shake. After ten picks, read the tally. Did red come most? Could anyone have been sure before a pick?

Chitra

For parents

Today's idea was chance. The bag held 6 red, 3 blue and 1 yellow marble, so a pick was more likely to be red, and never certain to be anything. Every marble went back in after its pick, so the bag never changed, and no colour was ever due.

Ask at dinner: when something is the most likely to happen, does that mean it will surely happen next? What would you count first to check?