jmc

We will use complementary probability: we will find the probability that no more than 1 baby speaks tomorrow, and then subtract the result from 1. There are two cases to consider: None of the babies will speak and that exactly 1 will speak.

1) The probability that none of the babies will speak tomorrow is ${\left(\frac{3}{4}\right)}^5=243/1024$.

2) The probability that exactly 1 will speak is $\left(\genfrac{}{}{0ex}{}{5}{1}\right){\left(\frac{3}{4}\right)}^4\left(\frac{1}{4}\right)=\frac{405}{1024}$.

The sum of these probabilities is $\frac{243+405}{1024}=\frac{648}{1024}=\frac{81}{128}$. Since the probability that no more than 1 baby will speak is $\frac{81}{128}$, the probability that more than 1 baby will speak is $1-\frac{81}{128}=\boxed{\frac{47}{128}}$.