Using a value converter is a solution.
<Grid x:Name="LayoutRoot" Background="White">
<Grid.Resources>
<local:BoolToStyleConverter x:Key="Correctness">
<local:BoolToStyleConverter.FalseValue>
<Style TargetType="TextBox">
<Setter Property="Background" Value="Salmon" />
</Style>
</local:BoolToStyleConverter.FalseValue>
<local:BoolToStyleConverter.TrueValue>
<Style TargetType="TextBox">
<Setter Property="Background" Value="AliceBlue" />
</Style>
</local:BoolToStyleConverter.TrueValue>
</local:BoolToStyleConverter>
</Grid.Resources>
<ItemsControl ItemsSource="{Binding}">
<ItemsControl.ItemTemplate>
<DataTemplate>
<StackPanel>
<TextBlock Text="{Binding Question}" />
<TextBox x:Name="Answer" Text="{Binding Answer, Mode=TwoWay}"
Style="{Binding IsCorrect, Converter={StaticResource Correctness}}" />
</StackPanel>
</DataTemplate>
</ItemsControl.ItemTemplate>
</ItemsControl>
</Grid>
BoolToStyleConverter, .
: -
public class BoolToStyleConverter : BoolToValueConverter<Style> { }