contestada

A family plans to have three children. The wife and husband are trying to determine the probabilities of the different gender outcomes for the children.
The husband thinks that the probability that the first child is a girl is greater than the probability that the first child is a girl and the second child is a girl. The wife disagrees. She thinks that the two probabilities are equal.
The sample space of possible outcomes is listed below. B represents a boy, and G represents a girl.
Who is correct, the husband or the wife?

Respuesta :

Using the probability concept, it is found that: [tex]p_{G} > p_{GG}[/tex], and thus, the husband is correct.

---------------------

  • 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.

---------------------

For two children, the sample space is:

B - B

B - G

G - B

G - G

  • 2 out of 4 outcomes in which the first child is a girl, thus, [tex]p_G = \frac{2}{4} = 0.5[/tex]
  • 1 out of 4 outcomes in which both are girls, thus [tex]p_{GG} = \frac{1}{4} = 0.25[/tex]

[tex]p_{G} > p_{GG}[/tex], and thus, the husband is correct.

A similar problem is given at https://brainly.com/question/14798120

Otras preguntas