118 VALUATION, DEPRECIATION AND THE RATE-BASE 
Let it again be assumed that practically no article of a large 
group, all of which have a ro-year probable life, will survive 20 
years or twice the probable life term, and that one-half or very 
nearly one-half of the failures occur within the two years just 
preceding and the two years just following the end of the prob- 
able life term. Then, according to the law of probability, and 
on the assumption that the failures may be bunched at the end 
of the successive years, there will be failures in each successive 
year as shown in Table 8. These are noted only to the nearest 
5 in 10,000, and in other respects are offered only as approxima- 
tions to demonstrate a law rather than the result of accurate 
computation. 
TABLE 8. FAILURES AND EXPECTANCY ACCORDING TO 
THE LAW OF PROBABILITY 
ON THE ASSUMPTION THAT NO ARTICLE SURVIVES TWICE THE PROBABLE 
Lire TERM. 10,000 ARTICLES. PROBABLE LIFE = 10 YEARS 
For 10,000 articles. Single article. 
Remaining num- Remaining service 
Number of . Eo Expect ib 
= EE SR 
15 10,000 100,000 10.00 
35 9,985 00,000 9.00 
| 8s 9,950 80,015 8.05 
| 180 9,865 70,065 7.11 
330 9,685 60,200 6.22 
550 9,355 50,515 5-40 
80s 8,805 41,160 4.78 
| 1065 8,000 32,355 4.04 
{£203 6,935 24,355 3.52 
1 1340 5,670 17,420 3.08 
0 1265 4,330 11,750 2:7% 
i 1065 3,065 7,420 2.42 
8os 2,000 4,355 2.18 
550 1,195 2,355 1.97 
; 330 645 1,160 1.80 
Ib 180 315 515 1.64 
ml 8x 135 | 200 I.50 
18 3s 50 65 I.25 
19 135 3 15 1.00 
20 [a o 0 2 
iy 1 
Yer