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## Quiz of the Month (September 2006)

### Hector C. Parr

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#### SOLUTION TO LAST MONTH'S QUIZ

```1.  16
2.  5
3.  8
4.  3```

Notes.

```1. Each marble can go into either box 1 or box 2.

2. Put either 0, 1, 2, 3 or 4 marbles in box 1.

3. Put 0 marbles in one box and 4 in the other (1 arrangement)
Put 1 marble in one box and 3 in the other (4 arrangements)
Put 2 marbles in each box (3 arrangements)

4. Put 0 marbles in one box and 4 in the other (1 arrangement)
Put 1 marble in one box and 3 in the other (1 arrangement)
Put 2 marbles in each box (1 arrangement)```

#### THIS MONTH'S QUIZ

A coin is tossed ten times.

1. Find the probability that the first six results are all heads.

2. Find the probability that the results include a run of exactly six consecutive heads.

3. Find the probability that the results include a run of at least six consecutive heads.

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