Weihnachtsmann rot

Challenge from 22. December

Christmas Baubles

Author: Jaques Resing

Project: 4TU.AMI

Challenge:

Santa Clause tells Ruprecht, “This box contains many blue and many red Christmas baubles. There are more blue baubles than red baubles.”
Ruprecht draws two baubles from the box, one of which is blue and one of which is red.
Santa Clause says, “Interesting! The probability to draw two baubles with different colors is 1/2.”

Ruprecht puts the two baubles back into the box, and then draws three baubles from the box. All three drawn baubles have the same color.
Santa Clause says, “Very interesting! The probability to draw three baubles with the same color is 1/4.”

Ruprecht puts the three baubles back into the box. Then he draws a red bauble, then a blue bauble, and finally another red bauble.
Santa Clause says, “Very, very interesting! The probability to draw red-blue-red is 0.123456, when rounded to six digits after the decimal point.”

Question: How many red and blue Christmas baubles are in the box (before the drawings)?

Illustration: Frauke Jansen

PDF download

Possible answers:

  1. There are 5,929 Christmas baubles in the box.

  2. There are 6,084 Christmas baubles in the box.

  3. There are 6,241 Christmas baubles in the box.

  4. There are 6,561 Christmas baubles in the box.

  5. There are 6,724 Christmas baubles in the box.

  6. There are 6,889 Christmas baubles in the box.

  7. There are 7,056 Christmas baubles in the box.

  8. There are 7,396 Christmas baubles in the box.

  9. There are 7,569 Christmas baubles in the box.

  10. There are 8,281 Christmas baubles in the box.

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