A family has 4 children. A tree diagram or systematic list can be used to show how many ways the children could have been born, from first born to last born.
Determine how many ways the family could have had one boy and 3 girls.
nothing
To determine how many ways the family could have had one boy and three girls, we can use a tree diagram or a systematic list.
Using a tree diagram:
1. Start with the first child, who could be either a boy (B) or a girl (G).
2. For each possible outcome of the first child, consider the second child. The second child could also be either a boy or a girl.
3. Repeat this process for the third and fourth children as well.
Here is the tree diagram:
B
/ \
B G
/ \ / \
B G B G
|
G
In this tree diagram, each branch represents a possible outcome for the family's children, from the first born to the last born.
By examining the tree diagram, we can see that there are 4 possible outcomes where the family has one boy and three girls:
1. B-G-G-G
2. G-B-G-G
3. G-G-B-G
4. G-G-G-B
Therefore, there are 4 ways the family could have had one boy and three girls.
Alternatively, we can also use a systematic list to determine the number of ways:
1. B-G-G-G
2. G-B-G-G
3. G-G-B-G
4. G-G-G-B
Again, we find that there are 4 ways the family could have had one boy and three girls.
To determine how many ways the family could have had one boy and three girls, we can use a tree diagram or a systematic list.
First, we need to consider the gender of the first child. There are two possibilities: a boy (B) or a girl (G).
If the first child is a boy (B), the second child can be a girl (G) or a boy (B). This gives us 2 possibilities.
If the first child is a girl (G), the second child can also be a girl (G) or a boy (B). Again, this gives us 2 possibilities.
For each of these possibilities, we continue the same process with the third and fourth child. Each child can be a girl (G) or a boy (B).
So, multiplying the number of possibilities at each step, we have:
2 (possibilities for the first child) * 2 (possibilities for the second child) * 2 (possibilities for the third child) * 2 (possibilities for the fourth child)
This equals 2^4 = 16.
Therefore, there are 16 different ways the family could have had one boy and three girls.
The one boy could be born first, second, third or last, 4 ways. The rest will be girls.
Cannot do a tree diagram here.