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The completed two-way table is attached.
Since 37 people were left-brain dominant, this leaves 63-37=26 that are right-brain dominant. 21 people were right-handed and right-brain dominant; this means that 26-21=5 people are left-handed and right-brain dominant.
Since 22 people were left-handed, this means 63-22=41 people are right handed. 21 of those people are right-brain dominant; this means that 41-21=20 people are right handed and left-brain dominant. Using this, we have that 37-20=17 people are left handed and left-brain dominant.
Since 37 people were left-brain dominant, this leaves 63-37=26 that are right-brain dominant. 21 people were right-handed and right-brain dominant; this means that 26-21=5 people are left-handed and right-brain dominant.
Since 22 people were left-handed, this means 63-22=41 people are right handed. 21 of those people are right-brain dominant; this means that 41-21=20 people are right handed and left-brain dominant. Using this, we have that 37-20=17 people are left handed and left-brain dominant.