The students in your class with three children in their families are asked to state the number of boys in the family. What are the possible numbers? If X is the number of boys minus the number of girls in each of these families, state all the possible values of X. Make a table of probability distribution.
Step by step please?
Thanks in advance :)
Number of children = 3
Possible number of boys = {0,1,2,3}
X=number of boys - number of girls
={-3,-1,1,3}
P(X)= probability of event X.
b g X P(X)
0 3 -3 1/8
1 2 -1 3/8
2 1 1 3/8
3 0 3 1/8
To determine the possible numbers of boys in the family, start by listing the different scenarios:
1. Family with three boys: In this scenario, all three children are boys.
2. Family with two boys and one girl: Here, the family has two boys and one girl.
3. Family with one boy and two girls: In this scenario, the family has one boy and two girls.
4. Family with three girls: Finally, the family has all three children being girls.
So, the possible numbers of boys are 3, 2, 1, or 0.
Now, let's calculate the values of X, which is the number of boys minus the number of girls in each family:
1. In the family with three boys, X = 3 - 0 = 3.
2. In the family with two boys and one girl, X = 2 - 1 = 1.
3. In the family with one boy and two girls, X = 1 - 2 = -1.
4. In the family with three girls, X = 0 - 3 = -3.
Now, let's create a table of probability distribution:
Family Configuration | Number of Boys (B) | Number of Girls (G) | Number of Children (C) | X = B - G
---------------------|--------------------|--------------------|----------------------|----------
Three boys | 3 | 0 | 3 | 3
Two boys, one girl | 2 | 1 | 3 | 1
One boy, two girls | 1 | 2 | 3 | -1
Three girls | 0 | 3 | 3 | -3
Please note that the probability distribution table cannot be determined without additional information, as you have not specified any probabilities associated with each family configuration.