Question

In a family of 7 children, what's the chance that 3 are one sex and 4 are the opposite sex?

o 2 x 1/7²
o (1/2⁷) x 2 x 7!/(3! x 4!)
o 1/2⁷
o 1/2⁷ x 7!/ (3! x 4!)

Answer 1

The chance of having 3 children of one sex and 4 of the opposite sex out of 7 is calculated using the combination formula multiplied by the two scenarios for sexes. This is represented by the formula ((1/2)^7) x 2 x (7!/(3! x 4!)). (option 2 is the correct answer).

Step-by-step explanation:

The student is inquiring about the probability of having three children of one sex and four of the opposite sex in a family with seven children. To calculate this, we use the basic principles of probability, focusing on the product and sum rules.

Since the sex of each child can be assumed to be independent of the others, and there's an equal chance of having a boy or a girl, we apply the following: the probability of having either a boy or girl for each child is ½.

So, the probability can be found using the combination formula to determine how the three children of one sex and four of the other can be arranged among seven births.

To do this, we calculate the number of ways to arrange three children of one sex and four of the other, which equates to 7!/(3! x 4!), and multiply by the probability of each such arrangement occurring, which is (1/2)7. Since there are two equally likely scenarios (either three boys and four girls, or three girls and four boys), we multiply the result by 2. Our final calculation is ((1/2)7) x 2 x (7!/(3! x 4!)).