in the doctrine of chances, is applied to any contingent event, and is capable of being reduced to the rules of computation. Thus a sum of money in expectation when a particular event happens, has a determinate value before that event happens; so that if a person is to receive any sum, e.g., £10l. when an event takes place which has an equal probability of happening and failing, the value of the expectation is half that sum or £5l.; and in all cases the expectation of obtaining any sum is estimated by multiplying the value of the sum expected by the fraction which represents the probability of obtaining it. The expectation of a person who has three chances in five of obtaining £10l. is equal to $\frac{3}{5} \times 100$ or £60l. and the probability of obtaining £10l. in this case is equal to $\frac{3}{5}$.

EXPECTATION of Life, signifies, in the doctrine of life annuities, that share or number of the years of human life, which a person of any given age may expect to enjoy on an equality of chance.

According to Mr Simpson, by the expectation of life we are not to understand that period which a person may have an equal chance of surviving, which is a different and more simple consideration; but the number of years at which the purchase of an annuity ought to be valued, granted on it without discount of money. There will be a greater or less difference in this number of years, in proportion to the various degrees of mortality to which the different stages of human life are exposed. Thus, it is more than an equal chance that an infant just come into the world, will not reach the age of 10 years; yet the expectation of life, or share of existence due to it, is almost 20 years upon an average. The reason of this vast difference is the excess of the probability of death in the first tender years of existence above that which respects the more advanced stages. If the numbers of those who die at every assignable period were always found to be on an equality, the two quantities already mentioned would be the same; but when these numbers constantly become less and less, the expectation must of consequence become the greater of the two.