What is the probability that a family with 4 children will have exactly 2 girls and 2 boys?
To calculate the probability of a family with 4 children having exactly 2 girls and 2 boys, you need to consider the total number of possible outcomes and the total number of favorable outcomes.
The total number of possible outcomes can be determined using the concept of a binomial distribution. In this case, each child has two possible outcomes, either being a girl or a boy. Since there are 4 children, the total number of possible outcomes is 2^4 = 16.
To determine the total number of favorable outcomes (i.e., families with exactly 2 girls and 2 boys), you can use combinations. The formula for combinations is given by: nCr = n! / (r!(n-r)!), where n is the total number of items and r is the number of items you want to choose.
In this case, you need to choose 2 girls out of 4 children, which can be calculated as 4C2 = 4! / (2!(4-2)!) = 6. Similarly, you need to choose 2 boys out of 4 children, which is also 4C2 = 6.
Finally, to calculate the probability, divide the total number of favorable outcomes by the total number of possible outcomes: probability = favorable outcomes / total outcomes.
So, the probability that a family with 4 children will have exactly 2 girls and 2 boys is 6 / 16, which simplifies to 3 / 8.
In summary, to calculate the probability:
1. Determine the total number of possible outcomes (2^4 = 16).
2. Calculate the total number of favorable outcomes using combinations (4C2 = 6 for girls and 4C2 = 6 for boys).
3. Divide the total number of favorable outcomes by the total number of possible outcomes to get the probability (6 / 16 = 3 / 8).