What is the percentage probability that all the children in a randomly selected family will be the same gender?  *1 pointA. 40%B. 25%C. 12.5%D. 10%

To determine the percentage probability that all the children in a randomly selected family will be the same gender, we need to consider the possible outcomes for the genders of the children.

1. Assume each child has an equal probability of being either a boy or a girl, which is 50% (or 0.5) for each gender.
2. For a family with multiple children, the probability that all children are the same gender can be calculated by considering the two possible scenarios: all boys or all girls.

Let's break it down step by step:

1. The probability that all children are boys:

   • For the first child: 0.5 (50%)
   • For the second child: 0.5 (50%)
   • For the third child: 0.5 (50%)
   • And so on...

   The combined probability for all children being boys is: $0.5 \times 0.5 \times 0.5 \times \ldots$ (depending on the number of children)

2. The probability that all children are girls is the same as the probability that all children are boys: $0.5 \times 0.5 \times 0.5 \times \ldots$

3. Since there are two scenarios (all boys or all girls), we add the probabilities of these two scenarios together.

For simplicity, let's consider a family with 2 children:

• Probability all are boys: $0.5 \times 0.5 = 0.25$ (25%)
• Probability all are girls: $0.5 \times 0.5 = 0.25$ (25%)

Adding these probabilities together: $0.25 + 0.25 = 0.5$ (50%)

However, the question asks for the probability that all children in a randomly selected family will be the same gender, without specifying the number of children. If we assume the family has more than 2 children, the probability decreases exponentially with each additional child.

For a general case with $n$ children:

• Probability all are boys: $(0.5)^n$
• Probability all are girls: $(0.5)^n$

Combined probability: $(0.5)^n + (0.5)^n = 2 \times (0.5)^n = (0.5)^{n-1}$

Given the options, the most reasonable assumption is that the family has 2 children, leading to a probability of 25%.

Therefore, the correct answer is: B. 25%