Respuesta :
Answer:
a) There is a 25% probability that a four-child family chosen at random will have three boys and a girl in the family.
b) There is a 50% probability of the youngest child being a girl.
c) There is a 25% probability that the oldest child and the youngest child in the family are both boys
Step-by-step explanation:
Probability:
What you want to happen is the desired outcome.
Everything that can happen iis the total outcomes.
The probability is the division of the number of possible outcomes by the number of total outcomes.
In our problem, there is:
-50% probability of giving birth to a boy.
-50% probability of giving birth to a girl.
There are the following babies:
B1 - B2 - B3 - B4
(a) Three boys and a girl in the family:
There is a 50% probability that each children is a boy and 50% that each children is a girl.
We want three boys and a girl, so we have to permutate these probabilities. It is a permutation of 4 elements(all the children), with 4(boys) and 1(girls) repetitions. So:
[tex]P = p^{4}_{3,1}*(0.5)^4 = \frac{4!}{3! 1!}*0.0625 = 0.25[/tex]
There is a 25% probability that a four-child family chosen at random will have three boys and a girl in the family.
(b) A youngest child in the family who is a girl
The probabilities are independent from each other. This is just the probability of B4 being a girl, that is 50%.
(c) An oldest child and a youngest child in the family who are both boys
The probabilities of B1 being a boy is 50% and of B4 being a boy is also 50%. So:
[tex]P = (0.5)*(0.5) = 0.25[/tex]
There is a 25% probability that the oldest child and the youngest child in the family are both boys
