A fair coin is used to simulate the gender of each child in a family with three children. a.) How could the faces of the coin be used to represent a child’s gender?

50/50 chance for all 3 children

Step-by-step explanation:

Let heads be the number of males

Let tails be the number of females.

There are 8 ways a family of 3 could be described.

H H H

H H T

H T H

H T T

T H H

T H T

T T H

T T T

So H T H means the oldest child is a male the middle child is a female and the youngest child is H which is a male.

  28 inches

Step-by-step explanation:

The point of intersection of the angle bisectors is the incenter. It is the center of a circle tangent to the three sides of the triangle. The circle has radius 2.

In the attached figure, we have labeled the points of tangency D, E, and F. We know that CE and CF are both of length 2, and we know that the points of tangency are the same distance from an external point where the tangents intersect. That means DA = FA and DB = EB.

The perimeter of the triangle is ...

  P = DA +DB +FA +EB +CF +CE

Using the above relations, this can be written as ...

  P = DA +DB +DA +DB +CF +CE = 2(DA +DB) +2(CE)

We are told that AB is 12 inches, so DA +DB = 12 inches. We also know that CE = 2 inches, so the perimeter is ...

  P = 2(12 in) + 2(2 in) = 28 in

The perimeter of triangle ABC is 28 inches.