In a certain​ country, the true probability of a baby being a girlgirl is 0.465. Among the next four randomly selected births in the​ country, what is the probability that at least one of them is a boy​?
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Part 1
The probability is enter your response here.
​(Round to three decimal places as​ needed.)

To solve this problem, we need to calculate the probability that at least one of the four babies is a boy. 

### Step-by-step solution:

1. **Probability of a girl**: The problem states that the probability of a baby being a girl is \( P(\text{girl}) = 0.465 \).
   
2. **Probability of a boy**: Since a baby can either be a girl or a boy, the probability of a boy is:
   \[
   P(\text{boy}) = 1 - P(\text{girl}) = 1 - 0.465 = 0.535
   \]

3. **At least one boy**: The easiest way to solve this is to first calculate the complementary event, which is the probability that **all four babies are girls**. Then, subtract that probability from 1 to get the probability of at least one boy.

   - The probability that all four babies are girls is:
     \[
     P(\text{all girls}) = (0.465)^4
     \]
   
4. **Complementary probability**: Now, the probability of at least one boy is:
   \[
   P(\text{at least one boy}) = 1 - P(\text{all girls})
   \]

Let me calculate this now.The probability that at least one of the four babies is a boy is \( 0.953 \) (rounded to three decimal places).

Would you like any further details or clarification?

Here are 5 related questions to expand on this topic:
1. What is the probability that all four babies are boys?
2. How would the probability change if there were five births instead of four?
3. What is the probability of exactly two boys among the four babies?
4. How can we calculate the probability of exactly one boy in four births?
5. How does the binomial distribution apply to this problem?

**Tip:** When solving probability problems, looking for complementary events can simplify the calculations significantly.

In a certain country, the true probability of a baby being a girl is 0.465. Among the next four randomly selected births in the country, what is the probability that at least one of them is a boy?

Calculate the probability that at least one of four randomly selected births is a boy, given the true probability of a girl is 0.465. This problem involves complementary events and probability rules, suitable for high school students studying Grades 9-12.

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