A family has three children.Assuming that the probability of having a boy is 0.5, what is the probability that at least one child is a boy?

Options

A. 0.875
B. 0.67
C. 0.5
D. 0.375

Explanation

To find the probability that at least one child is a boy in a family with three children, we can follow these steps:

### Step 1: Understand the total possible outcomes
When a family has three children, each child can either be a boy (B) or a girl (G). Therefore, the total possible combinations of children can be represented as follows:
- BBB
- BBG
- BGB
- BGG
- GBB
- GBG
- GGB
- GGG

This gives us a total of \(2^3 = 8\) possible outcomes.

### Step 2: Calculate the probability of having zero boys
The only scenario where there are zero boys is when all three children are girls (GGG).

The probability of having a girl for each child is 0.5. Thus, the probability of having three girls (zero boys) is calculated as follows:
\[ P(\text{zero boys}) = P(G) \times P(G) \times P(G) = 0.5 \times 0.5 \times 0.5 = 0.125 \]

### Step 3: Calculate the probability of having at least one boy
To find the probability of having at least one boy, we can use the complement rule:
\[ P(\text{at least one boy}) = 1 - P(\text{zero boys}) \]
Substituting the value we calculated in Step 2:
\[ P(\text{at least one boy}) = 1 - 0.125 = 0.875 \]

### Final Answer
Thus, the probability that at least one child is a boy is \(0.875\).

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