I have only glossed over the other answers, but there is a cool way to approach this question that nobody mentioned...

For the sake of this exercise, let's say that you are part of a household with 100 people. All cousins live together, I don't know. You're just one big family who share the budget.

If one family member gets sick, it's alright. The other 99 are still healthy.

Let's say there is a p=0.1 chance any one member of the family is sick for a year. That member cannot take money home during that full year. Let's see how many family members will be sick that year.

The answer is this binomial distribution: http://postimg.org/image/vkn76o9sd/

P(N <= 20) = 0.9991924. There is a 0.9991924 probability that 20 members of the family are sick in a given year. Or, in other words, P(N > 20) = 0.0008. After N>40, my 64-bit does not have enough precision to show the probability. It is effectively zero.

Now, I am going to flip the graphic so that is shows the probability of each person being healthy. I am also adding a x-axis at the top showing how much income each family member has: http://postimg.org/image/cprhxbum9/

Now, contrast that with living alone and having a probability=10% of getting sick where your income drops to 0, which would be this discrete probability distribution: http://postimg.org/image/5tdb44vhr/. (Sorry for the ugly graphics :P)

Nobody lives in huge families anymore. The huge family is the insurance company.

In the real world, this is why big rent-a-car companies do not buy insurance. They are like the big family. If some car goes to the shop, no worries, the other make up the income. But small rent-a-car companies to buy insurance.