Question

1) A certain couple is equally likely to have either a boy child or a girl child. If the family has three children, let X denote the number of girls. (10-points) a) Identify the possible values of the random variable X. b) Determine the probability distribution of X c) Use random variable notation to represent the event that the couple has at most 2 girls AND also determine that probability

**please explain and write out each step you
do.**

Answer #1

1. If a couple plans to have 4 children, what is the probability
that there will be at least one girl? Assume boys and girls are
equally likely.
2. Find the probability of a couple having a baby boy when their
4th child is born, given that the first three children were all
boys. Assume boys and girls are equally likely.

Suppose that in 4-child families, each child is equally likely
to be a boy or a girl, independently of the others. Which would
then be more common, 4-child families with 2 boys and 2 girls, or 4
child families with different numbers of boys and girls? What would
be the relative frequencies? (Detailed answer using binomial
distribution)

Assume that girls and boys are equally likely and the event
"having a girl" does not affect the future/past probability of
"having a boy" and vice versa. Also, there are no twins. You see a
woman walking on the street with a girl. She tells you that she has
three children and that the girl with her is her daughter. a) What
is the probability that she has two boys? Incorrect: Your answer is
incorrect. (enter a fraction) b) What...

A
young couple decides to keep having children until they have a
girl. Assuming a boy or a girl are equi-probable possibilities in
the birth of every child and the gender of every child is
independent of the previous, what would be the expected number of
children the couple would have when the first girl is born? What is
the probability that the fourth child would be the first
girl?

A couple is planning on having 5 children and the probability of
having a girl is 0.517. If we define the random variable to be the
number of girls in 5 births, then the probability the couple will
have less than 3 girls is 0.468.
Is the event the couple will have less than 3 girls an unusual
event? Briefly explain.

The random variable X is the number of girls of four children
born to a couple that is equally likely to have either a boy or a
girl. Its probability distribution is as follows
Q24
(a) µ = E(X) = (Round your answer to one decimal place)
(b) σ(X) = (Round your answer to one decimal place)
c) Among all families with four children, what is the average
number of boys?
(Round your answer to one decimal place)

A couple plans to have children until they get a girl, but they
agree they will not have more than three children, even if all are
boys. Assume that the probability of having a girl is
0.50.5.
Let X be a random variable indicating how many children the
couple will have. Find the standard deviation of the random
variable X.
x
11
22
33
P(X=x)
0.5000.500
0.2500.250
0.250

Problem: Suppose that a couple will have 3 children. Assume that
the probability of having a girl is .487 and the probability of
having a boy is .513. Also assume that x is a random variable for
the number of girls and find the probability where x is 0, 1, 2, or
3. In order words, answer the following probability questions.
What is the probability that none of the three children will be
girls?
What is the probability that exactly...

Problem: Suppose that a couple will have 3 children. Assume that
the probability of having a girl is .487 and the probability of
having a boy is .513. Also assume that x is a random variable for
the number of girls and find the probability where x is 0, 1, 2, or
3. In order words, answer the following probability questions. What
is the probability that none of the three children will be girls?
What is the probability that exactly...

A family has 19 children. Assume boys and girls are equally
likely and that the gender of one child does not affect the gender
of another child. Find the following probabilities:
a) The probability of the family having no girls.
b) The probability of the family having exactly nine girls.
c) The probability of the family having exactly seven boys.
(Please show all work.)

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