Question

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 weightweight outcomes​ (using o for overweight and u for underweighto for overweight and u for underweight​) of two children.
b. assuming that the outcomes listed in part​ (a) were equally​ likely, find the probability of getting two underweightunderweight children.
c. find the probability of getting exactly one overweightoverweight

Answer 1

There are two choices for each child: overweight (o) or underweight (u). So if the first child is o the next can be o or u. If the first is u the second can be o or u. This gives four possibilities. Here the first child is the letter noted first and the second is the one listed second:
OO
OU
UO
UU

There are 4 outcomes and if each is equally likely then the probability of each is 1/4. Thus the probability of UU is 1/4

The probability of one underweight and one over weight is 1/2 because in two of the outcomes listed above there is one O and one U (namely OU and UO). Since there are 4 outcomes the probability is 2/4 = 1/2