Question 145
Throwing an ankle-bone results in four positions – horse, camel, sheep and goat – with equal probability. A player throws four ankle-bones and receives the following number of points depending on the positions.
| Position | Score |
|----------------------------------|-------|
| Four horses | 100 |
| Four camels | 90 |
| Three horses, one sheep | 75 |
| Three camels, one goat | 65 |
| One horse, three sheep | 25 |
| One camel, three goats | 15 |
| One of each | 8 |
| Four sheep | 4 |
| Four goats | 4 |
| Two sheep, two goats | 2 |
How many throws are needed on average in order to reach at least 100 points cumulatively?
| Position | Score |
|----------------------------------|-------|
| Four horses | 100 |
| Four camels | 90 |
| Three horses, one sheep | 75 |
| Three camels, one goat | 65 |
| One horse, three sheep | 25 |
| One camel, three goats | 15 |
| One of each | 8 |
| Four sheep | 4 |
| Four goats | 4 |
| Two sheep, two goats | 2 |
How many throws are needed on average in order to reach at least 100 points cumulatively?