A couple intends to have four children. Assume that having a boy and girl is equally likely event.
a) List sample space
b) Find the probability that couple has two boys and two girls;
c) Find the probability that couple has at least one boy
5. A couple plans to have 3 children. Find the possible ways the couple can have 3 children.
- 1a3b+3a2b1+3a1b2+1 a0b3
1a3= 1 case with boy, boy, boy
3a2b1= 3 cases with 2 boys and a girl
3a1b2=3 cases with a boy and 2 girls
1b3= 1 case of girl, girl and girl.
a) To list the sample space, we need to consider the possible outcomes for each child. Since each child can be either a boy or a girl, there are two possible outcomes for each child. Therefore, the sample space can be represented as:
BBGG
BGBG
GBBG
BGGB
GBGB
GGBB
BBBB
GGGG
Each letter represents the gender of one child, with 'B' representing a boy and 'G' representing a girl.
b) To find the probability that the couple has two boys and two girls, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes.
In this case, there are three favorable outcomes:
BBGG
BGBG
GBBG
And there are eight total possible outcomes (listed in the sample space).
Therefore, the probability is:
P(two boys and two girls) = favorable outcomes / total outcomes = 3/8
c) To find the probability that the couple has at least one boy, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes.
In this case, the favorable outcomes are all the outcomes in which there is at least one boy. From the sample space, the outcomes that satisfy this condition are:
BBGG
BGBG
GBBG
BGGB
GBGB
GGBB
BBBB
There are seven favorable outcomes.
Therefore, the probability is:
P(at least one boy) = favorable outcomes / total outcomes = 7/8
12345
finish the chart
BBBB
BBBG
BBGB
BBGG
.....
GGGG --- you should have 16 of these
count the number of cases for each of your events,
then divide by 16 to the prob.