To calculate the probability that at least one of the seven randomly selected births is a boy, we can use the complement rule.

1. Given:

   • The probability of a baby being a girl, $P(\text{Girl}) = 0.474$.
   • Therefore, the probability of a baby being a boy is $P(\text{Boy}) = 1 - P(\text{Girl}) = 1 - 0.474 = 0.526$.

2. Complementary Event:

   • The complementary event to "at least one boy" is "no boys," which means all seven babies are girls. We can calculate the probability of this event and subtract it from 1.

3. Probability of no boys (all girls): $P(\text{All girls}) = P(\text{Girl})^7 = 0.474^7$

4. Probability of at least one boy: $P(\text{At least one boy}) = 1 - P(\text{All girls})$

Now, let's compute the value.

$P(\text{All girls}) = 0.474^7 \approx 0.0079$ $P(\text{At least one boy}) = 1 - 0.0079 \approx 0.9921$

Thus, the probability that at least one of the seven babies is a boy is approximately 0.992.

Final Answer:

The probability is approximately 0.992 (rounded to three decimal places).

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Would you like more details on the calculation or have any other questions?

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Follow-up Questions:

1. How can the complement rule be applied to other probability problems?
2. What is the effect of increasing the number of births on the probability of having at least one boy?
3. How would this change if the probability of having a girl were different (e.g., 0.6)?
4. How can we calculate the exact probability of having exactly 3 boys out of 7 births?
5. What is the relationship between independent events and the probability of combined outcomes?

Tip: When calculating probabilities involving "at least one," it's often easier to use the complement rule—first calculate the probability of the opposite event, and then subtract from 1!