Ballots are paid for:
a. by political parties
b. by the candidates
c.
at public expense
d. individually at the polling place

The answer is:

a) 0.12521 or 12.521%

b) 0.04736 or 4.736%

Explanation:

a) Because the number of soldiers killed by horse kicks each year in each corps in the Prussian cavalry followed a Poisson distribution with a mean of 0.61.

The probability of one death in a corps in a year:

P(k = 1 in a year) = (0.61^1 x e^(-0.61))/ 1! = 0.33144

The probability of no death in a corps in a year:

P(k = 0 in a year) = (0.61^0 x e^(-0.61))/ 0! = 0.54335

The probability of more than one death in a corps in a year:

P(k > 1 in a year) = 1 - P(k = 1 in a year) - P(k = 0 in a year)

= 1 - 0.33144 - 0.54335 = 0.12521 or 12.521%

b) The probability of no deaths in a corps over five years:

P(k=0 in 5 years) = e^(-λ) with λ as the average number of soldiers killed by horse kicks in a 5 year interval.

λ = 0.61 x 5 = 3.05 => P(k=0 in 5 years) = e^(-3.05) = 0.04736 or 4.736%