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 \(\frac34\)