To solve this, let's break down the problem step by step.

The probability of a baby being a girl is given as $P(\text{Girl}) = 0.474$.

Since the probability of a baby being a boy is simply the complement of the probability of being a girl, we have: $P(\text{Boy}) = 1 - P(\text{Girl}) = 1 - 0.474 = 0.526$

The Problem

We are asked to find the probability that at least one of the seven randomly selected births results in a boy.

Complementary Event Approach

The easiest way to approach this is by finding the probability of the complementary event — that is, the probability that none of the seven births results in a boy (i.e., all of them are girls), and then subtracting that from 1.

The probability that all seven births result in girls is: $P(\text{All Girls}) = (P(\text{Girl}))^7 = 0.474^7$

Now, the probability that at least one of the seven births is a boy is the complement of the above event: $P(\text{At Least One Boy}) = 1 - P(\text{All Girls})$ $P(\text{At Least One Boy}) = 1 - 0.474^7$

Let me calculate this for you.

$P(\text{At Least One Boy}) = 1 - 0.474^7 \approx 1 - 0.005052 = 0.994948$

Final Answer:

The probability that at least one of the seven births results in a boy is approximately 0.995 (rounded to three decimal places).

Would you like more explanation or assistance with anything else? Here are some related questions:

1. How does the probability change if the number of selected births increases to 10?
2. What if the probability of a baby being a girl was 0.5 instead of 0.474?
3. How do you calculate the probability for multiple events like this in a more general sense?
4. How does this complement rule apply to other probability problems?
5. Can you use this method to calculate the probability of "at least one success" in other types of problems (e.g., defective products)?

Tip: Always look for complementary events when calculating probabilities involving "at least one" or "none" situations. It often simplifies the calculation!