Final answer:
The probability that no girls and 3 boys will be chosen is 1/55 or approximately 1.82%.
Step-by-step explanation:
To find the probability that no girls and 3 boys will be chosen, we need to determine the total number of possible outcomes and the number of favorable outcomes.
There are a total of 12 children (8 girls + 4 boys) in the family. Since 3 children are being chosen, the total number of possible outcomes is the combination of 12 children taken 3 at a time, which is denoted as C(12, 3) = 220.
The number of favorable outcomes is choosing 3 boys from the 4 available boys, which is denoted as C(4, 3) = 4.
Therefore, the probability of choosing no girls and 3 boys is 4/220 = 1/55, which can be reduced to approximately 0.0182 or 1.82%.