A sample of four families with three children each was taken.find the probability that one family has two girls,two families have three girls and one family has three boys.

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To find the probability, we need to consider the total number of possible outcomes and the number of favorable outcomes.

First, let's calculate the total number of possible outcomes. Each family has three children, and each child can be either a boy or a girl. Therefore, there are 2^3 = 8 possible outcomes for each family.

Since there are four families, the total number of possible outcomes will be 8^4 = 4096.

Next, let's calculate the number of favorable outcomes. We want one family to have two girls, two families to have three girls each, and one family to have three boys.

To calculate the number of favorable outcomes, we can break it down into three steps:

Step 1: Choose the family with two girls:
There are four families, and we need to choose one to have two girls. This can be done in C(4, 1) = 4 ways.

Step 2: Choose the families with three girls:
Now, we need to choose two out of the remaining three families to have three girls each. This can be done in C(3, 2) = 3 ways.

Step 3: Determine the possible outcomes for each family:
For the family with two girls, there are C(3,2) = 3 possible outcomes (GGG, GGB, or GBG).
For each of the two families with three girls, there is only one possible outcome (GGG).

Therefore, the total number of favorable outcomes is 4 * 3 * 3 * 1 * 1 = 36.

Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:

Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes
= 36 / 4096
= 9 / 1024

Therefore, the probability that one family has two girls, two families have three girls each, and one family has three boys is 9/1024.