Question

Suppose a couple planned to have three children. Let X be the number of boys the couple has. (a) List all possible arrangements of aris and boys. For example, if the couple had 2 girs and then a boy, then type GGB. (Separate each item in your list with a comma): (b) List the sample space for X. (f.e. List the possible values that X may take separated by commas): ( (c) What is the probability that X=1 ? (d) Find the probability that the couple has three boys:

Answer 1

Let's break down the problem step by step:

(a) List all possible arrangements of girls (G) and boys (B) for a family planning to have three children:

1. BBB

2. BBG

3. BGB

4. GBB

5. BGG

6. GBG

7. GGB

8. GGG

(b) List the sample space for X, which is the possible values that X (the number of boys) may take:

X can take on the values: 0, 1, 2, 3

(c) To find the probability that X=1, we need to count the number of outcomes where there is exactly 1 boy (B) and 2 girls (G). From the list in part (a), we can see that there are three such outcomes: BBG, BGB, and GBB. There are a total of 8 possible outcomes. So, the probability that X=1 is 3/8.

(d) To find the probability that the couple has three boys (X=3), we need to count the number of outcomes where all three children are boys (BBB). There is only one such outcome, and there are still 8 possible outcomes in total. So, the probability that the couple has three boys is 1/8.

Explanation: