Let, the event of giving birth to a son be B.
And the event of giving birth to a girl be G.
Then, P(B) = \(\frac12\) and P(G) = \(\frac12\)
A probability tree diagram for giving birth to two children by a married couple is given below.
Possible Outcomes
To find, \(P(\overline{B\cap B)}\)
Here, \(P(\overline{B\cap B)}\) = P(B) x P(B) = \(\frac12\times\frac14=\frac14\)
and \(P(\overline{B\cap B)}\) = 1 - \(P(\overline{B\cap B)}\) = \(1-\frac14\)
= \(\frac34\)
Therefore, the probability of giving birth to at least a daughter is \(\frac34\)