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## Quiz of the Month (June 2004)

### Hector C. Parr

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#### SOLUTION TO LAST MONTH'S QUIZ

```    1.  17/36
2.  5/17
3.  5/9```

Notes

```1. The probability that Smith walked, Smith said he walked, and
Jones also said he walked, which we denote by p(WWW),
= 1/4 * 2/3 * 2/3 = 4/36
Likewise,  p(WBW) = 1/4 * 1/3 * 1/3 = 1/36
And   p(BWW) = 3/4 * 1/3 * 2/3 = 6/36
And   p(BBW) = 3/4 * 2/3 * 1/3 = 6/36
Total = 17/36

2. Probability Jones said Smith walked = 17/36 (as above).
Probability Smith walked and Jones said he walked
= p(WWW) + p(WBW) = 4/36 + 1/36 = 5/36
So required probability = 5/36 / 17/36 = 5/17

3. Similarly, p(WWW) + p(WBW) + p(BWB) + p(BBB)
= 4/36 + 1/36 + 3/36 + 12/36 = 20/36 = 5/9
```

#### THIS MONTH'S QUIZ

1. Two walls of a room meet at right angles to form a corner. A straight stick lies on the floor with each end in contact with a wall. The mid-point of the stick is 9 cm from one wall and 12 cm from the other. How long is the stick?

2. A circular table stands in contact with both walls. A point on its circumference is 8 cm from one wall and 16 cm from the other. What is the diameter of the table?

3. A child's tennis ball lies in the corner touching both walls. A point on its surface is 1 cm from one wall, 4 cm from the other wall, and 5 cm from the floor. What is the diameter of the ball?

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