If a couple were planning to have three children, the sample space summarizing the gender outcomes would be: bbb, bbg, bgb, bgg, gbb, gbg, ggb, ggg. a. Construct a similar sample space for the possible hair color outcomes (using b for brown dash haired and r for red dash headed) of two children. b. Assuming that the outcomes listed in part (a) were equally likely, find the probability of getting two red dash headed children. c. Find the probability of getting exactly one brown dash haired child and one red dash headed child.

a. Construct a similar sample space for the possible hair color outcomes (using b for brown dash haired and r for red dash headed) of two children.

We can build this sample space like a truth table.

So:

bb

br

rb

rr

b. Assuming that the outcomes listed in part (a) were equally likely, find the probability of getting two red dash headed children

There are four possibilities in (a). The only possibility that we get two red dash headed children is rr.

The probability formula is the number of desired outcomes divided by the number of total outcomes. Out of four outcomes, one is desired. So:

[tex]P = \frac{1}{4}[/tex]

[tex]P = 0.25[/tex]

There is a 25% probability of getting two red dash headed children.

c. Find the probability of getting exactly one brown dash haired child and one red dash headed child.

There are four possibilities in (a). There are two possibilities in which we get exactly one brown dash haired child and one red dash headed child.

So, there is two desired outcomes out of four total outcomes. So

[tex]P = \frac{2}{4}[/tex]

[tex]P = 0.50[/tex]

There is a 50% probability of getting exactly one brown dash haired child and one red dash headed child.