Suppose that a couple decided to continue to have children until they have one g

Question

Suppose that a couple decided to continue to have children until they have one girl. Assume P(girl)=0.4 and let X denote the number of children that they have. a) Find the probability mass function P(X = x) = f(x) with all possible values of x. b) Find the probability that the couple has at least 3 children, that is P(X > = 3) c) Suppose that a few years later the couple has two boys and continue to have children until they have a girl. Find the conditional probability that the couple has at least two additional children (hence at least 5 children total), given that they have at least three children (2 boys +), that is P(X > =3 + 2 | X > = 2+1). d) Compare your answer from b) and c). Explain the result in a sentence that can be understood by someone with no statistical background.

Explanation / Answer

a) P(X=x) =till x-1 th children all are boy*xth child is girl =(0.6)x-1*(0.4)

b) P(X>=3) =0.62 =0.36

c)P(X>=5|X>=3) =P(X>=5)/P(X>=3)= 0.64/0.62 =0.36

d) here we can understand that geometric distribution is memory less and probabilty of evidence does not depend on prior event

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.