- #1

fog37

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- TL;DR Summary
- probability in two-child problem

Hello,

This is a classic problem in basic statistics: find the probability of two children of different gender being born, one after the other from the same mother. The sample space is ##{GG, BB, GB, BG}## with B= boy and G=girl.

CASE 1: the event "a boy is born if the first child who was born is also a boy" has the probability ##\frac {1}{2}##. The event is ##BB## and the reduced sample space is ##{BB, BG}##.

CASE 2: the event "a boy is born and there is at least a boy" has the probability ##\frac {1}{3}## since the reduces sample space is ##{BB, , GB, BG}##.

In the first case, the order matters, i.e. ##GB \neq BG## But the order does not matter in case 2 meaning that ##GB=BG##

Is my understanding correct?

Thanks!

This is a classic problem in basic statistics: find the probability of two children of different gender being born, one after the other from the same mother. The sample space is ##{GG, BB, GB, BG}## with B= boy and G=girl.

CASE 1: the event "a boy is born if the first child who was born is also a boy" has the probability ##\frac {1}{2}##. The event is ##BB## and the reduced sample space is ##{BB, BG}##.

CASE 2: the event "a boy is born and there is at least a boy" has the probability ##\frac {1}{3}## since the reduces sample space is ##{BB, , GB, BG}##.

In the first case, the order matters, i.e. ##GB \neq BG## But the order does not matter in case 2 meaning that ##GB=BG##

Is my understanding correct?

Thanks!