Carter dies on January 1,2016.A joint return election is made in 2016 and Marjorie properly qualifies as a surviving spouse for the two following years.Marjorie has one child that she claims as a dependent for this same period.The number of personal and dependency exemptions allowed Marjorie in 2016 and in 2017,respectively:

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In 2016, Carter and Marjorie can file a joint return which will have a personal exemption of 2. Since Marjorie's child is also claimed as a dependent, she can claim an additional dependency exemption for a total of 3 exemptions. 
In 2017 and 2018, Marjorie can use the qualifying widow(er) filing status which allows her to use the joint return tax rates and rules for two years after her spouse's death. This means that she will have a personal exemption of 1 for each year, but since she still has a dependent child she can claim an additional dependency exemption for a total of 2 exemptions each year. Therefore, the total number of exemptions allowed to Marjorie in 2016 is 3 (2 personal, 1 dependency) and in 2017 is 2 (1 personal, 1 dependency).

Carter Dies on January 1,2016