19.20 Gambling in ancient Rome. Tossing four astragali was the most popular game of chance in Roman times. Many throws of a present-day sheep’s astragalus show that the approximate probability distribution for the four sides of the bone that can land uppermost are
| Outcome | Probability |
| Narrow flat side of bone | 110 |
| Broad concave side of bone | 410 |
| Broad convex side of bone | 410 |
| Narrow hollow side of bone | 110 |
The best throw of four astragali was the “Venus,” when all four uppermost sides were different.
(a) Explain how to simulate the throw of a single astragalus. Then explain how to simulate throwing four astragali independently of each other.
(b) Simulate 25 throws of four astragali. Estimate the probability of throwing a Venus. Be sure to say what part of Table A you used.