#!/usr/bin/env python
# coding: utf-8

# # Les intervalles de fluctuation

# ## Les paramètres

# In[1]:


import math 
p=0.7
n=100


# ## En seconde

# In[2]:


k=1/math.sqrt(n)

a=p-k
b=p+k

print(f"I=[{a:.8f} ; {b:.8f}]")


# ## En terminale

# In[3]:


k=1.96*math.sqrt(p*(1-p))/math.sqrt(n)

a=p-k
b=p+k

print(f"I=[{a:.8f} ; {b:.8f}]")


# ## En Première

# In[4]:


#------------------------------------------------------
def fact(n) :
    "Calcule factoriel n."
    if (n==0) :
        return 1
    else :
        p=1
        for k in range(1,n+1):
            p=p*k
        return p

#------------------------------------------------------
def combin (n,k):
    "Calcule  k parmi n."
    p=1
    for i in range(n-k+1,n+1) :
        p=p*i
    return p//fact(k)



def binomial(n,p,k):
    "Calcule p(x=k)"
    return math.exp(math.log(combin(n,k))+k*math.log(p)+(n-k)*math.log(1-p))

cumul=0
d=dict() # dictionaire des (k,p(x=k))
for k in range(n+1):
    cumul+=binomial(n,p,k)
    d[k]=cumul

for (c,v) in d.items() : # recherche de a
    if v>0.025 :
        a=c
        break
        
for (c,v) in d.items() : # recherche de b
    if v>0.975 :
        b=c
        break

print(f"I=[{a/n:.8f} ; {b/n:.8f}]")


# In[16]:


d_bas=dict((c,v) for (c,v) in d.items() if a-10<c<a+10)
for (c,v) in d_bas.items():
    print(f"{c:4d} | {v:.6f}")
    if (c==a-1):
        print("------------------ 0,025")


# In[14]:


d_haut=dict((c,v) for (c,v) in d.items() if b-10<c<b+10)
for (c,v) in d_haut.items():
    print(f"{c:4d} | {v:.6f}")
    if (c==b-1):
        print("------------------ 0,975")


# In[ ]: