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## Quiz of the Month (February 2007)

### Hector C. Parr

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#### SOLUTION TO LAST MONTH'S QUIZ

```  1.  3/20
2.  3/11
3.  7/38```

Notes.
```  1. 3 equi-probable houses out of 20.

2. 9 equi-probable children out of 33.

3. No. of possible pairs = 20 * 19 / 2 = 190

No. of pairs, both with 0 children =  6
No. of pairs, both with 1 child    = 15
No. of pairs, both with 2 children = 10
No. of pairs, both with 3 children =  3
No. of pairs, both with 4 children =  1
Total   = 35
So probability = 35/190.```

#### THIS MONTH'S QUIZ

1. A fair six-sided die is rolled a large number of times. What is the expected average of the scores ?

2. Two fair six-sided dice are rolled together a large number of times. The lesser of the two scores (or the common score if they are equal) is recorded each time. What is the expected average of the recorded scores ?

3. Three fair six-sided dice are rolled together a large number of times. The least of the three scores is recorded each time. What is the expected average of the recorded scores ?

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