A couple plans to have three children. What is the probability that they have at least one girl?
1 - P(no girls) = 1 - P(all boys) = 1 - (1/2)^3 = _____
To calculate the probability of having at least one girl, we need to find the complement of the probability of having all boys.
First, let's consider the possible outcomes for each child. Each child can be either a boy (B) or a girl (G). Since there are two possible outcomes for each child, and the couple plans to have three children, the total number of possible outcomes is 2^3 = 8.
Now, let's determine the number of outcomes where all the children are boys. There is only one combination where all three children are boys: BBB.
Since there are 8 possible outcomes and only 1 outcome where all the children are boys, the number of outcomes where at least one child is a girl is 8 - 1 = 7.
Therefore, the probability of having at least one girl is 7/8, or 0.875 (87.5%).
Explanation, step by step:
1. Determine the number of possible outcomes for each child. In this case, there are two possible outcomes: boy (B) or girl (G).
2. Since the couple plans to have three children, we need to find the total number of possible outcomes by multiplying the number of outcomes for each child. In this case, it's 2^3 = 8.
3. Identify the number of outcomes where all the children are boys. In this case, there is only one combination: BBB.
4. Calculate the number of outcomes where at least one child is a girl by subtracting the number of outcomes where all children are boys from the total number of outcomes. In this case, it's 8 - 1 = 7.
5. Calculate the probability by dividing the number of outcomes where at least one child is a girl by the total number of outcomes: 7/8 = 0.875 or 87.5%.