Why does access to safe water and improved sanitation affect a country's life expectancy?

Answer 1

To understand the what happens in an entire country it might be enough to consider what happens to the life expectancy of just one person who has access to safe water or improved sanitation.

First, what is life expectancy? The life expectancy for a person is calculated by adding up the products of all ages that the person might achieve and the probabilities that the person might achieve those ages. Let's assume that no-one lives beyond, say, 100, and that we are willing to ignore ages in months. Then we have ages, 1, 2, 3, 4, 5, 6, ..., 100. In some countries, most unfortunately, the probability of living to age 6 might be only 0.5 so the product for this age would be 6 * 0.5 = 3. The probability of living to age 10 might be only 0.2, so the product would be 10 * 0.2 = 0.02. We would calculate these products for each of the 100 ages and add them, then divide by 100, to obtain the life expectancy

Now, with access to safe water a child would be far less likely to die before age 10. In other words that probability of survival of 0.2 would be considerably larger, say, 0.7, and the corresponding product would be larger. Simply put, the person would live longer because he would be less likely to be killed by some disease transmitted in unsafe water. In fact, unsafe water is a hazard to people at all ages; therefore, the probabilities used in those products would be somewhat bigger for all ages. The idea is the same for improved sanitation.