{
"metadata": {
"name": "",
"signature": "sha256:41b66ed6dbdebdc3dd934ef963f179576dd8d1497050c4ff934c3909d90dbee3"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 12: Probability"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example Problem 12.1, Page Number 283"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example Problem 12.2, Page Number 284"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from fractions import Fraction\n",
"\n",
"#Variable Declaration\n",
"n = 52 #Total cards\n",
"nheart = 13 #Number of cards with hearts\n",
"\n",
"#Calculations\n",
"Pe = Fraction(nheart,n)\n",
"\n",
"#Results\n",
"print 'Probability of one (heart)card picked from a std. stack of %d cards is'%n,Pe"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Probability of one (heart)card picked from a std. stack of 52 cards is 1/4\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example Problem 12.3, Page Number 285"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example Problem 12.4, Page Number 285"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable Declaration\n",
"n1 = 2 #Two spin states for 1st electron in orbit 1\n",
"n2 = 2 #Two spin states for 2nd electron in orbit 2\n",
"\n",
"#Calculation\n",
"M = n1*n1\n",
"\n",
"#Results\n",
"print 'Possible spin states for excited state are %2d'%M"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Possible spin states for excited state are 4\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example Problem 12.5, Page Number 286"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import factorial\n",
"\n",
"#Variable Declaration\n",
"n = 12 #Total Number of players \n",
"j = 5 #Number player those can play match\n",
"\n",
"#Calculation\n",
"P = factorial(n)/factorial(n-j)\n",
"\n",
"#Results\n",
"print 'Maximum Possible permutations for 5 player to play are %8d'%P"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Maximum Possible permutations for 5 player to play are 95040\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example Problem 12.6, Page Number 287"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import factorial\n",
"\n",
"#Variable Declaration\n",
"n = 52 #Number of cards in std . pack\n",
"j = 5 #Number of cards in subset\n",
"\n",
"#Calculation\n",
"C = factorial(n)/(factorial(j)*factorial(n-j))\n",
"\n",
"#Results\n",
"print 'Maximum Possible 5-card combinations are %8d'%C"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Maximum Possible 5-card combinations are 2598960\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example Problem 12.7, Page Number 288"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import factorial\n",
"\n",
"#Variable Declaration\n",
"x = 6 #Number of electrons\n",
"n = 2 #Number of states\n",
"\n",
"#Calculation\n",
"P = factorial(x)/(factorial(n)*factorial(x-n))\n",
"\n",
"#Results\n",
"print 'Total number of quantum states are %3d'%P"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Total number of quantum states are 15\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example Problem 12.8, Page Number 289"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import factorial\n",
"from fractions import Fraction\n",
"\n",
"#Variable Declaration\n",
"n = 50 #Number of separate experiments\n",
"j1 = 25 #Number of sucessful expt with heads up\n",
"j2 = 10 #Number of sucessful expt with heads up\n",
"\n",
"#Calculation\n",
"C25 = factorial(n)/(factorial(j1)*factorial(n-j1))\n",
"PE25 = Fraction(1,2)**j1\n",
"PEC25 = (1-Fraction(1,2))**(n-j1)\n",
"P25 = C25*PE25*PEC25\n",
"\n",
"C10 = factorial(n)/(factorial(j2)*factorial(n-j2))\n",
"PE10 = Fraction(1,2)**j2\n",
"PEC10 = (1-Fraction(1,2))**(n-j2)\n",
"P10 = C10*PE10*PEC10\n",
"\n",
"#Results\n",
"print 'Probability of getting 25 head out of 50 tossing is %4.3f'%(float(P25))\n",
"print 'Probability of getting 10 head out of 50 tossing is %4.3e'%(float(P10))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Probability of getting 25 head out of 50 tossing is 0.112\n",
"Probability of getting 10 head out of 50 tossing is 9.124e-06\n"
]
}
],
"prompt_number": 14
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example Problem 12.9, Page Number 290"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import factorial, log\n",
"#Variable Declaration\n",
"N = [10,50,100] #Valures for N\n",
"\n",
"#Calculations\n",
"print ' N ln(N!) ln(N!)sterling Error'\n",
"for i in N:\n",
" lnN = log(factorial(i))\n",
" lnNs = i*log(i)-i\n",
" err = abs(lnN-lnNs)\n",
" print '%3d %5.2f %5.2f %4.2f'%(i,lnN,lnNs, err)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" N ln(N!) ln(N!)sterling Error\n",
" 10 15.10 13.03 2.08\n",
" 50 148.48 145.60 2.88\n",
"100 363.74 360.52 3.22\n"
]
}
],
"prompt_number": 37
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example Problem 12.10, Page Number 293"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from fractions import Fraction\n",
"\n",
"#Variable Declaration\n",
"fi = 1 #Probability of receiving any card\n",
"n = 52 #Number od Cards\n",
"\n",
"#Calculations\n",
"sum = 0\n",
"for i in range(52):\n",
" sum = sum + fi\n",
"\n",
"Pxi = Fraction(fi,sum)\n",
"\n",
"#Results\n",
"print 'Probability of receiving any card', Pxi"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Probability of receiving any card 1/52\n"
]
}
],
"prompt_number": 39
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example Problem 12.11, Page Number 295"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import exp\n",
"from scipy import integrate\n",
"#Variable Declaration\n",
"\n",
"#Calculations\n",
"fun = lambda x: exp(-0.05*x)\n",
"Pt = 0\n",
"for i in range(0,101):\n",
" Pt = Pt + fun(i)\n",
" \n",
"Ptot = integrate.quad(fun, 0.0, 100.)\n",
"\n",
"#Results\n",
"print 'Sum of Px considering it as discrete function %4.1f'%Pt\n",
"print 'Sum of Px considering it as contineous function %4.1f'%Ptot[0]"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(19.865241060018292, 2.205484801456136e-13)\n",
"Sum of Px considering it as discrete function 20.4\n",
"Sum of Px considering it as contineous function 19.9\n"
]
}
],
"prompt_number": 47
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example Problem 12.12, Page Number 296"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from sympy import *\n",
"\n",
"#Variable Declaration\n",
"r = Symbol('r') #Radius of inner circle\n",
"C = [5,2,0]\n",
"#Calculations\n",
"A1 = pi*r**2\n",
"A2 = pi*(2*r)**2 - A1\n",
"A3 = pi*(3*r)**2 - (A1 + A2)\n",
"At = A1 + A2 + A3\n",
"f1 = A1/At\n",
"f2 = A2/At\n",
"f3 = A3/At\n",
"sf = f1 + f2 + f3\n",
"\n",
"ns = (f1*C[0]+f2*C[1]+f3*C[2])/sf\n",
"\n",
"#Results\n",
"print 'A1, A2, A3: ', A1, A2, A3\n",
"print 'f1, f2, f3: ', f1,f2,f3\n",
"print 'Average payout $', round(float(ns),2)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"A1, A2, A3: pi*r**2 3*pi*r**2 5*pi*r**2\n",
"f1, f2, f3: 1/9 1/3 5/9\n",
"Average payout $ 1.22\n"
]
}
],
"prompt_number": 60
}
],
"metadata": {}
}
]
}