Which of the following policies is likely to pay a sum to surviving children after both parents have died?

The joint survivorship life policy is designed to provide a payout after the death of the second insured individual. In this case, when both parents have passed away, the policy would pay a death benefit to the designated beneficiaries, typically the surviving children. This type of policy ensures that the financial protection intended for dependents is secured even in the unfortunate event that both parents are no longer living.

Other options do not provide the same benefits in this context. A family income policy primarily provides income replacement for a specified period following the death of the first parent, focusing on immediate needs rather than a sum for surviving children after both parents have died. A joint life policy covers two individuals but typically pays out upon the death of the first insured, not considering a payout for surviving children after both are deceased. A family policy combines multiple types of coverage for family members but does not guarantee a payout specifically intended for surviving children after both parents' deaths. Thus, the joint survivorship life policy distinctly serves the need for providing financial support to surviving children after both parents have passed away.