Question

Please read the following prompt carefully: "About 48% of all births result in a girl. Suppose a couple is planning to have three children." Determine the following values by rounding to the nearest indicated decimal place. Please type your solution in the text entry boxes provided. a. What is the probability of the first- born child being a boy? (Use the form X.XX) b. What is the probability of the first- born child being a girl? (Use the form X.XX) c. What is the probability of the second-born child being a boy? (Use the form X.XX)

Answer 1

a.) What is the probability of first born child being a boy?

Answer: 0.52

Reason:

Probability of first child being girl = 48% =0.48

Probability of first child being boy= 1 - 0.48 =0.52

b.) What is the probability of first born child being a girl?

Answer: 0.48

Reason:

Probability of first child being girl = 48% =0.48

c.) What is the probability of second born child being a boy?

Answer: 0.52

Reason: The probability of boy is independent of first born, second born or third born.

d.) What is the probability of second born child being a boy?

Answer: 0.48

Reason: The probability of girl is independent of first born, second born or third born.

e.) What is the probability of third born child being a boy?

Answer: 0.52

Reason: The probability of boy is independent of first born, second born or third born.

f.) What is the probability of third born child being a boy?

Answer: 0.48

Reason: The probability of girl is independent of first born, second born or third born.

g.) What is the probability of having three boys?

Answer: 0.14

Reason: The probability of three boys is = 0.52*0.52*0.52 = 0.14

h.) What is the probability of having two boys and one girl?

Answer: 0.39

Reason:

Probability of two boys and one girl is given by

$=^3C_2*0.52^2*(1-0.52)^{(3-2)}$

$=3*0.52^2*(0.48)^{1}$

=0.39

i) What is the probability of having one boys and two girls?

Answer: 0.36

Reason:

Probability of one boys and two girl is given by

$=^3C_1*0.52^1*(1-0.52)^{(3-1)}$

$=6*0.52*(0.48)^{2}$

=0.36

j.)What is the probability of having three girls?

Answer: 0.11

Reason:

Probability of 3 girls = 0.48*0.48*0.48 = 0.11

k.) What is the probability of having at least one boy?

Answer: 0.89

Reason:

Probability of having at least one boy = 1- Probability of all 3 girls = 1 - 0.11 = 0.89

l.) What is the probability of having at least one girl?

Answer: 0.86

Reason:

Probability of having at least one girl = 1- Probability of all 3 boys = 1 - 0.14 = 0.86

m.) What is the probability of having at least two boys?

Answer: 0.53

Reason:

Probability of having at least two boys = Probability of all 3 boys + Probability of two boys and 1 girl

= 0.14 + 0.39 = 0.53

n.) What is the probability of having at least two girls?

Answer: 0.47

Reason:

Probability of having at least two girls= Probability of all 3 girls + Probability of one boy and 2 girl

= 0.11 + 0.36 = 0.47

o) What is the probability of having at most one boy?

Answer: 0.47

Reason:

Probability of having at most one boy= Probability of all 3 girls + Probability of one boy and 2 girl

= 0.11 + 0.36 = 0.47

p) What is the probability of having at most one girl?

Answer: 0.53

Reason:

Probability of having at most one girl = Probability of all 3 boys + Probability of two boys and 1 girl

= 0.14 + 0.39 = 0.53

q.) What is the probability of having at most two boys?

Answer: 0.86

Reason:

Probability of having at most two boys = 1 - Probability of all 3 boys = 1 - 0.14 = 0.86

r.) What is the probability of having at most two girls?

Answer: 0.89

Reason:

Probability of having at most two girls = 1 - Probability of all 3 girls = 1 - 0.11 = 0.89