Draw Blind

The cloth bag holds exactly the marbles drawn next to it. You may not look inside, so you reach in blindly and put nothing back.
Which marble are you most likely to draw? The kind there is the most of in the bag. If marbles were taken out first, count again.
With "sure", the worst luck counts. To be sure of a dark marble, you draw all the others first in the worst case. Only the next one has to be dark.
To be sure of two the same, you draw a different kind each time in the worst case. Then the next marble is bound to be a match.
Work out the unlucky run, write the number in the box, or circle the kind that is in front.

Example

?24You reach in blindly. Which marbleare you most likely to draw?Circle it.
?342How many marbles must you draw atleast to be sure to have one darkmarble?8

For parents

What does this exercise practice?

The child practices telling "possible", "likely" and "sure" apart. This builds a feel for data and chance without fractions. The chance grows with the count, and "sure" means playing through the worst course of events. That is a first proof in a second grader's language - everything else first, then one more.

Common pitfalls

The most common mistake is to mix up "sure" and "likely". With luck you pick the right marble at once, but only what works even with the worst luck is sure. The second stumbling block is the wrong number. For "sure of a dark one" it is not how many dark ones there are that counts but how many others. The third is forgetting to adjust the numbers next to the bag after marbles were taken out.

How to practice at home

Fill a sock with building bricks in two or three colors. The child predicts which color will come up most, then draws ten times, putting the brick back each time. Then the bad-luck question comes next. How many bricks do you have to draw at least to be sure of two the same? Try it and count.

Related: Certain, possible or impossible?, The Dice Sum Table

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