Question

Suppose that a family has five children, consisting of three girls and two boys. Call the girls Abigail, Brianna, and Courtney; call the boys Duane and Evan. Suppose further that two of these children are to be selected at random.

List the sample space of all possible pairs of these five children.

a.

Determine the probability that one child of each gender will be selected.

Report your answer to two decimal places; e.g., 0.xx

b. Determine the probability that two boys will be selected. Report your answer to two decimal places

c. Determine the probability that two girls will be selected. Report your answer to two decimal places

d. Determine the expected value of the number of girls who will be selected. Report answer to one decimal place.

e. Determine the expected value of the number of boys who will be selected. Report your answer to one decimal place

Answer #1

"In a family of 6 children, what is the probability of 4 boys
and two girls? "

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.)

Suppose 44% of the children in a school are girls. If a sample
of 545 children is selected, what is the probability that the
sample proportion of girls will be less than 43% ? Round your
answer to four decimal places.

1) The random variable X represents the number of girls
in a family of 6 children. Assuming that the event of having boys
and girls are equally likely. Construct the discrete probability
distribution for the random variable X and plot your results. For
the number of girls, determine the expected mean and standard
deviation.

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)

Boys and Girls: Suppose a couple plans to have
two children and the probability of having a girl is 0.50.
(a) What is the sample space for the gender outcomes?
{bb, bg, gb, gg}{bb, bg, gg} {bb,
gg}{b,g}
(b) What is the probability that the couple has one boy and one
girl?
1
2
3
4
1
4
1
3
(c) What is the probability that the couple will have at least one
girl?
1
4
1
2
3...

Let the random variable x represent the number of girls in a
family with three children. Assume the probability of a child being
a girl is 0.42. The table on the right describes the probability of
having x number of girls. Determine whether the table describes a
probability distribution. If it does, find the mean and standard
deviation. Is it unusual for a family of three children to consist
of three girls?
x | P(x)
0 | 0.195
1 |...

If the ratio of boys born to girls born is 105 to 100, and if 6
children are born in a certain hospital in a day, what is the
probability that 4 of them are boys? (Round your answer to four
decimal places.)

Mean and Standard Deviation of Boys or Girls
Worldwide, the proportion of babies who are girls is about 0.49 .
Let the random variable X represent the number of girls in
fivechildren. Find the mean and standard deviation of this random
variable.
Enter the exact answer for the mean, and round your answer for the
standard deviation to three decimal places.
μ=
sd=

Children Suppose a family has two children and the youngest is a
girl. What is the probability that both children are girls?

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