Question

Create both a tree diagram AND sample space of all possible boy/girl births in a family of three kids.

1. How many outcomes are there?
2. What is the probability of all three kids being boys?
3. What is the chance of only the middle kid being a girl?
4. What is the probability of there being at least two boys?
5. What is the chance of there being at most one girl?

Answer 1

Answer: Sample space: {BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG}

1. 8 outcomes in total

2. 1/8 or 0.125

3. 1/2 or 0.5

4. 1/2 or 0.5

5. 3/8 or 0.375

Explanation:

1. As shown by the sample space and the tree diagram, there are 8 total possibilities.

2. There is only a 1/8 or 0.125 chance of there being all boys, which is BBB

3. There are 4 outcomes that allow the middle child to be a girl, and 4/8 = 1/2. There will only be a girl middle child with BGB, GGG, BGG, and GGB.

4. We can think of at least as meaning no less than two boys, which includes two to three boys. The only outcomes that have either two or three boys is BBB, BBG, BGB, GBB. 4/8 = 1/2.

5. We can think of at most as meaning no more than one girl. The only outcomes that have only one girl are BBG, BGB, and GBB, which is 3/8.