a couple is planning to have three children. Find the probability that the couple will have:

a.) 2 girls and 1 boy?
b.) 2 girls followed by a boy?
c.) at least 1 girl?

please answer my question thank you very much, have a good day!

There are 8 ways to have B G

a)2 girls and 1 boy ---> GGB GBG BGG
Prob = 3/8

b) 2 girls followed by boy --->GGB
prob = 1/8

c) at least one girl, means exclude BBB
prob = 1 - 1/8 = 7/8

To find the probability of having a certain combination of children, we need to assume that the probability of having a boy or a girl is equal, i.e., 0.5. Let's solve each part separately:

a.) Probability of having 2 girls and 1 boy:
The couple can have either a girl (G) or a boy (B) as their first child, the same possibilities for the second child and only one option for the third child (opposite gender to the other two). There are a total of 2 * 2 * 1 = 4 possible outcomes. So, the probability is 1/4.

b.) Probability of having 2 girls followed by a boy:
Again, the couple can have either a girl (G) or a boy (B) as their first child, the same possibilities for the second child, and only one option for the third child (boy). There are a total of 2 * 2 * 1 = 4 possible outcomes. So, the probability is 1/4.

c.) Probability of having at least 1 girl:
The couple can have either a girl (G) or a boy (B) as their first child, either a girl or a boy as their second child, and either a girl or a boy as their third child. There are a total of 2 * 2 * 2 = 8 possible outcomes. Out of these, 3 outcomes have all boys (BBB), and the remaining 5 outcomes have at least 1 girl. So, the probability of having at least 1 girl is 5/8.

Note: These probabilities assume that the gender of each child is independent of the others, and that the probability of having a boy or girl is exactly 0.5. In reality, the gender of a child is determined by a combination of genetic factors.