${}_{87}{}^{221}\mathrm{Ra}$ undergoes radioactive decay with a half life of 4 days. The probability that a Ra nucleus will disintegrate in 8 days is:

The probability at time $t$ that a radioactive nucleus will disintegrate is defined as:

$P=\frac{N_0-N}{N_0}$

where $N_0$ = number of nuclei present initially at  $t=0$.

$N=$number of nuclei left at time $t$.

Now 8 days = 2 half lives. 

After 2 half lives, the number of nuclei left will be: 

$N=\frac{N_0}{{\left(2\right)}^2}=\frac{N_0}{4}$

$\therefore$ $P=\frac{N_0-{\displaystyle \frac{N_0}{4}}}{N_0}=\frac{3}{4}$