An individual should most likely purchase insurance for a risk that poses high standard of living risk and is infrequent.
Why and what does it mean?
Infrequent: If something that doesnt occur often, so you should take insurance on it. If it occurs often, its too expensive and you cant insure against it, which means you should avoid or reduce the risk. Pre-mature death is infrequent so you can insure against it.
High standard of living risk: Means the family spends lots of money on living expenses. If the primary bread winner dies, the family needs the insurance to continue their standard of living.
Assess risk exposure vs risk tolerance and then decide which strategy to take, there are four general strategies transfer, avoid, reduce or retain the risk. Purchasing insurance transfers the risk to the insurer but has a negative E®, and generally are a bad deal. So if it is a situation where risk exposure is way higher than acceptable risk tolerance then you transfer the risk or avoid it
Do they really?
edited to add an extra s there 
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