Question

Suppose that the genders of the three children of a family are soon to be revealed. An outcome is represented by a string of the sort

GBB

(meaning the oldest child is a girl, the second oldest is a boy, and the youngest is a boy).

The

8

outcomes are listed below. Assume that each outcome has the same probability.

Complete the following. Write your answers as fractions.

(a)Check the outcomes for each of the three events below. Then, enter the probability of each event.

	Outcomes								Probability
	BBB	BBG	BGB	BGG	GBB	GBG	GGB	GGG
Event X: The first child is a boy
Event Y: Exactly two children are girls
Event X and Y: The first child is a boy and exactly two children are girls

(b)Suppose the first child is a boy. (That is, Event

X

occurs.) This will limit the possible outcomes. From the remaining outcomes, check the outcomes for Event

Y

. Then, enter the probability that Event

Y

occurs given that Event

X

occurs.

	Outcomes given the first child is a boy								Probability
	BBB	BBG	BGB	BGG
Event Y: Exactly two children are girls

(c)Give the following probabilities and select the correct option below.

PX and YPX	=
PY|X	=
PX and YPX	▼?	PY|X

Answer 1