Final answer:
To calculate the probability of selecting a family with three male children, you need to consider all the possible outcomes and their respective probabilities. The probability of selecting a family with at least three male children is 1.
Step-by-step explanation:
The probability of selecting a family with at least three male children can be found by determining the probability of each outcome and summing them up. Let's analyze the possible outcomes:
- MMM: This represents a family with three male children. Since there is only one outcome, the probability of selecting this family is 1/8.
- MMF: This represents a family with two male children and one female child. There are three possible arrangements for this outcome: MMF, MFM, and FMM. So, the probability of selecting this family is 3/8.
- MFM: This represents a family with one male child and two female children. Similarly, there are three possible arrangements for this outcome. So, the probability of selecting this family is 3/8.
- FMF: This represents a family with one female child and two male children. Again, there are three possible arrangements. So, the probability of selecting this family is 3/8.
- FFF: This represents a family with three female children. Just like MMM, there is only one outcome, so the probability of selecting this family is 1/8.
To find the probability of selecting a family with at least three male children, we add the probabilities of the outcomes MMM, MMF, MFM, and FMF:
Probability = 1/8 + 3/8 + 3/8 + 1/8 = 8/8 = 1