The probability of picking out a boy's name from the hat can be calculated by dividing the number of boy names by the total number of names in the hat. In this case, there are 10 boy names and 30 total names (10 boys + 20 girls). Therefore, the probability of picking out a boy's name is 10/30 or 1/3, which can also be expressed as approximately 0.333 or 33.33%.
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