import numpy as np,pylab as pl,numpy.random as nr
def darts(r1=2,r2=10,n=5000):
if r2<r1:return ValueError
XY=r2*(2*nr.random([2,n])-1)
cond0=XY[0]**2+XY[1]**2<=r2**2
XY=np.squeeze(XY[:,np.where(cond0)])
cond1=XY[0]**2+XY[1]**2<r1**2
cond2=XY[0]**2+XY[1]**2>r1**2
XY1=np.squeeze(XY[:,np.where(cond1)])
XY2=np.squeeze(XY[:,np.where(cond2)])
large_circle=pl.Circle((0,0),r2,color='b',alpha=.3)
small_circle=pl.Circle((0,0),r1,color='r',alpha=.5)
fig,ax=pl.subplots(figsize=(5,5))
ax.set_xlim(-r2-1,r2+1); ax.set_ylim(-r2-1,r2+1)
ax.add_artist(large_circle); ax.add_artist(small_circle)
ax.scatter(XY1[0],XY1[1],c='black',s=5)
ax.scatter(XY2[0],XY2[1],c='grey',s=5)
ax.set_title('Darts',fontsize=18) num=XY.shape[1]; res=XY2.shape[1]/num
print(f'Results of {num} experiments: {res}') print('The probability that the dart '+\ f'did not hit the red circle = {result_prob}') pl.tight_layout(); pl.show()
