Question

1. A simple model for human offspring is that each child is equally likely to be male or female. With this model, a three-child family can be thought of as three random determinations of sex, in order.

a. What are the 8 possible outcomes? What is the probability of each?

b. What outcomes make up the event “the oldest child is a daughter”? What is the event’s probability?

c. What outcomes make up the event “the family has one daughter and two sons”? What is its probability?

d. What is the complement of the event in part (c)? List the outcomes in it and describe it in words. What is its probability?

e. What outcomes make up the event “the family has at least one daughter”? What is its probability?

Answer 1

here let a girl and boy child are represented by G and B

a) hence 8 possible outcomes: {GGG,GGB,GBG,BGG,GBB,BGB,BBG,BBB}

as each outcome is equally likely; probability of each outcome=1/8

b)

P( oldest child is a daughter )=4/8=1/2 (as 4 events {GGG,GBG,BGG,BBG} have older child as a daughter)

c)

P( the family has one daughter and two sons )=3/8 ( 3 events {GBB ; BGB , BBG})

d)

complement probability =1-3/8=5/8

events are {GGG,GGB,GBG,BGG,BBB}

this represent events with having exactly 0,2 or 3 daughters.

e)

outcomes in the family has at least one daughter are ={ GGG,GGB,GBG,BGG,GBB,BGB,BBG }

probability of above event =7/8