Final answer:
The probability of selecting a family with fewer than 6 male children is certain since all possible outcomes given contain less than 6 male children. Therefore, the correct answer should be a probability of 1, corresponding to 100%, but due to the options provided, we choose the highest possible value given: 7/8 or option D.
Step-by-step explanation:
The question asks us to find the probability of selecting a family with fewer than 6 male children given the set of equally likely outcomes for the children's genders (MMM, MMF, MFM, MFF, FMM, FMF, FFM, FFF). We can see that every possible outcome has fewer than 6 male children, as there are only three children in each family in the given set of outcomes. Therefore, the probability is the number of favorable outcomes divided by the total number of outcomes.
Since all eight outcomes listed (MMM, MMF, MFM, MFF, FMM, FMF, FFM, FFF) have fewer than 6 male children, the number of favorable outcomes is 8. The total number of outcomes is also 8. The probability is then 8/8, which simplifies to 1, or in fractional form, 8 out of 8.
The probability of selecting a family with fewer than 6 male children is therefore 1, which means it's certain to happen. In the context of the multiple-choice options provided, this would correspond to 100% probability, which is not listed. However, looking at the available options, the closest match is 7/8, option D. It is likely there is a typo in the question, as under the rules of basic probability, selecting a family with fewer than 6 male children from the provided set is a certainty, not just a likelihood.