Respuesta :
Answer:
a) {GGG, GGB, GBG, BGG, BBG, BGB, GBB, BBB}
b) {0,1,2,3}
c)
[tex]P(X=2) = \dfrac{3}{8}[/tex]
d)
[tex]P(\text{3 boys}) = \dfrac{1}{8}[/tex]
Step-by-step explanation:
We are given the following in the question:
Suppose a couple planned to have three children. Let X be the number of girls the couple has.
a) possible arrangements of girls and boys
Sample space:
{GGG, GGB, GBG, BGG, BBG, BGB, GBB, BBB}
b) sample space for X
X is the number of girls couple has. Thus, X can take the values 0, 1, 2 and 3 that is 0 girls, 1 girl, 2 girls and three girls from three children.
Sample space: {0,1,2,3}
c) probability that X=2
P(X=2)
That is we have to compute the probability that couple has exactly two girls.
[tex]\text{Probability} = \displaystyle\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}[/tex]
Favorable outcome: {GGB, GBG, BGG}
[tex]P(X=2) =\dfrac{3}{8}[/tex]
d) probability that the couple have three boys.
Favorable outcome: {BBB}
[tex]P(BBB) = \dfrac{1}{8}[/tex]
Using probability concepts, it is found that:
a) The possible arrangements are: {GGG, GGB, GBG, GBB, BGG, BGB, BBG, BBB}
b) The sample space is: S = {0, 1, 2, 3}.
c) [tex]\frac{3}{8}[/tex] probability that X=2.
d) [tex]\frac{1}{8}[/tex] probability that the couple have three boys.
- A probability is the number of desired outcomes divided by the number of total outcomes.
- The sample space is the set that contains all possible outcomes.
Item a:
Taking into account the different orders, then:
GGG, GGB, GBG, GBB, BGG, BGB, BBG, BBB.
Then, the possible arrangements is: {GGG, GGB, GBG, GBB, BGG, BGB, BBG, BBB}.
Item b:
The sample space is the number of girls, which is: S = {0, 1, 2, 3}.
Item c:
Out of 8 outcomes, 3 have two girls(GGB, GBG, BGG), thus:
[tex]p = \frac{3}{8}[/tex]
[tex]\frac{3}{8}[/tex] probability that X=2.
Item d:
Out of 8 outcomes, 1 has three boys, which is BBB, thus:
[tex]\frac{1}{8}[/tex] probability that the couple have three boys.
A similar problem is given at https://brainly.com/question/15006554
