We are given the probability of a baby being a girl as $P(\text{girl}) = 0.481$.

The probability of a baby being a boy is then: $P(\text{boy}) = 1 - P(\text{girl}) = 1 - 0.481 = 0.519$

We are asked to find the probability that at least one of the next four randomly selected births is a boy.

Step 1: Approach using Complementary Probability

The easiest way to solve this is to use complementary probability. Instead of directly finding the probability of at least one boy, we can calculate the probability of the complementary event (i.e., no boys at all), and subtract this from 1.

• The probability of no boys (i.e., all four babies are girls) is: $P(\text{no boys}) = P(\text{girl})^4 = 0.481^4$

• The probability of at least one boy is then: $P(\text{at least one boy}) = 1 - P(\text{no boys}) = 1 - 0.481^4$

Step 2: Calculation

Now we will calculate $0.481^4$ and subtract it from 1 to get the desired probability.

$0.481^4 \approx 0.0542$ $P(\text{at least one boy}) = 1 - 0.0542 = 0.9458$

Final Answer:

The probability that at least one of the four babies is a boy is approximately 0.946 (rounded to three decimal places).

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Would you like further clarification on the steps, or do you have another question?

Here are 5 related questions you might find interesting:

1. What is the probability that all four babies are girls?
2. If the probability of a boy were 0.6, how would this affect the calculation?
3. How do complementary probabilities work in other real-life scenarios?
4. What is the formula for binomial probability and how does it apply to this question?
5. How would you adjust this calculation if there were more or fewer babies?

Tip: Remember, complement probability is often useful in situations where calculating the desired outcome directly is complex!