Final answer:
The probability that a couple will have at least one boy when they decide to have 3 children is calculated by subtracting the probability of having three girls (0.125) from 1, resulting in 0.875 or 87.5%.
Step-by-step explanation:
The question asks for the probability that a couple will have at least one boy if they decide to have 3 children. To calculate this, one approach is to find the probability of the event that they do not have any boys and subtract this from 1 (since it's the only alternative to having at least one boy).
Assuming the probability of having a boy or a girl is equal (50% chance for each), and the gender of each child is independent of the others, the probability of having a girl is 0.5. The probability of having three girls in a row is then (0.5)3, which is 0.125. Therefore, the probability of having at least one boy is 1 - 0.125, which equals 0.875 or 87.5%.
Probability of Having At Least One Boy
- Calculate the probability of having three girls: (0.5)3 = 0.125
- Subtract this from 1 to get the probability of having at least one boy: 1 - 0.125 = 0.875
This kind of probability calculation is crucial for understanding the chances of different genetic outcomes when planning a family or studying genetic probability.