Assume a family is planning to have three children.
A. What is is the probablity of a family having 2 girls.
B. The probablity of a family having at least 1 boy.
C. List the sample space using a B for Boy and G for girl (Hint there should be 8 possible outcomes).
a) prob (2 girls out of 3) = C(3,2) (1/2)^2 (1/2)
= 3(1/8) = 3/8
b) at least 1 boy --- no "all girls"
prob (all girls) = 1/8
prob (at least 1 boy) = 1 - 1/8 = 7/8
c)
BBB
BBG
BGB
GBB
GGB
GBG
BGG
GGG
To calculate the probabilities, we'll start by creating the sample space for all possible outcomes.
C. Sample Space:
To list all possible outcomes, we can use a tree diagram. Assuming each child has an equal probability of being a boy or a girl, we would have the following eight possibilities:
1. B-B-B
2. B-B-G
3. B-G-B
4. G-B-B
5. G-G-B
6. G-B-G
7. B-G-G
8. G-G-G
Now let's move on to answering the specific questions:
A. Probability of a family having 2 girls:
To calculate this probability, we need to count the number of outcomes where the family has 2 girls (GG) and divide it by the total number of possible outcomes.
From the sample space above, we can see that there are three outcomes with 2 girls (GG): G-G-B, G-G-G, and G-B-G. Therefore, the probability of having 2 girls is 3/8, or 0.375 (or 37.5%).
B. Probability of a family having at least 1 boy:
To calculate this probability, we need to count the number of outcomes where the family has at least 1 boy and divide it by the total number of possible outcomes.
From the sample space above, we can see that there are seven outcomes with at least 1 boy (B-B-B, B-B-G, B-G-B, G-B-B, G-G-B, B-G-G, and G-G-G). Therefore, the probability of having at least 1 boy is 7/8, or 0.875 (or 87.5%).