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Civil War Estimates of the Union Army's strength and losses for the battle of Gettysburg are given in the following table, where strength is the number of soldiers immediately preceding the battle and loss indicates a soldier who was killed, wounded, captured, or missing. Source: Regimental Strengths and Losses of Gettysburg.
Unit | Strength | Loss |
I Corps (Reynolds) | 12,222 | 6059 |
II Corps (Hancock) | 11,347 | 4369 |
III Corps (Sickles) | 10,675 | 4211 |
V Corps (Sykes) | 10,907 | 2187 |
VI Corps (Sedgwick) | 13,596 | 242 |
XI Corps (Howard) | 9188 | 3801 |
XII Corps (Slocum) | 9788 | 1082 |
Cavalry (Pleasonton) | 11,851 | 610 |
Artillery (Tyler) | 2376 | 242 |
Total | 91,950 | 22,803 |
(a) Find the probability that a randomly selected Union soldier was from the XI Corps.
(b) Find the probability that a soldier was lost in the battle.
(e) Find the probability that a I Corps soldier was lost in the battle.
(d) Which group had the highest probability of not being lost in the battle?
(e) Which group had the highest probability of loss?
(f) Explain why these probabilities vary.

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