# conditional probability ?

#### osamastat

##### Member
Ignoring twins and other births , assume babies are born at hospital are independent events with the probability that a baby is a boy and the probability that a baby is a girl both equal to 0.5 , if the first two children born are girls , what is the probability that the next born child is a boy ?

#### AngleWyrm

##### Active Member
Assume babies are born at hospital are independent events
This means there is no sequential ordering, no dependence on the outcome of prior steps. They are equivalent to simultaneous.

if the first two children born are girls
This question has been framed as if it refers to a sequence where there is a dependence on prior outcomes. By your own definition they are independent and thus not dependent, but the follow up question seems to conjecture there's a dependency.

Let's adjust that just a little, to merely identifying the individual births
How many possible outcomes are there to flipping three coins? 2^3=8.
How many of those eight possible outcomes are you counting as a success?

A AND B AND (NOT C)

For the sake of contrast, drawing cards from a deck is a sequence that depends on the outcome of prior steps. If I draw Seven of Spades, then the next draw will not be Seven of Spades.

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