Final answer:
The probability that at least one of the three children born to a couple is male is calculated by finding the complement of the event where all three children are female. With the probability of each birth resulting in a female being 1/2, the probability of having three females in a row is 1/8. Subtracting this from 1 gives us a probability of 7/8, or 87.5%, for having at least one male child.
Step-by-step explanation:
To calculate the probability that at least one of the three children born to a couple is male, we can utilize the concept of complementary probability, which deals with the probability of the occurrence of the complementary event (all children being female) and subtracting it from one. Given that the probability of having a male or female child is equally likely (50% each), let's determine the probability of not having a male child across three consecutive births.
The probability of having a female child in each birth is 1/2. To find the probability of having three female children in a row, we would multiply these probabilities together:
Probability of 3 females = (1/2) * (1/2) * (1/2) = 1/8
Now, the probability that at least one of the three children is male is the complement of all being females. Therefore:
Probability of at least 1 male = 1 - Probability of 3 females = 1 - 1/8 = 7/8
The probability that at least one of the three children born to a couple is male is 7/8 or 87.5%.