Question: 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                      1/10

Broad concave side of bone                 4/10

Broad concex side of bone                   4/10

Narrow hollow side of bone                  1/10

The best throw of four astragali was the "Venus," when all the 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.