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    "### Data Analysis\n",
    "#### Probability, standard terms: sample space, trial, outcome, and event  \n",
    "<hr>\n",
    "https://github.com/ostad-ai/Machine-Learning\n",
    "<br> Explanation: https://www.pinterest.com/HamedShahHosseini/Machine-Learning/Data-Visualization"
   ]
  },
  {
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   "source": [
    "For set operaions in Python, see our repository for Python\n",
    "<br> https://github.com/ostad-ai/Python-Everything"
   ]
  },
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     "text": [
      "Two events:\n",
      "{1, 3, 5} ; {2, 4, 6}\n",
      "The two events are mutually exclusive.\n"
     ]
    }
   ],
   "source": [
    "# Experiment: rolling a dice\n",
    "rolling_dice={1,2,3,4,5,6} #sample space\n",
    "odd_number_event={1,3,5}  #event of odd numbers\n",
    "# operator ^ does symmetric set difference\n",
    "even_number_event=rolling_dice^odd_number_event\n",
    "print('Two events:')\n",
    "print(odd_number_event,';',even_number_event)\n",
    "# operator & does intersection among the sets\n",
    "if odd_number_event & even_number_event==set():\n",
    "    print('The two events are mutually exclusive.')\n",
    "else:\n",
    "    print('The two events are NOT mutually exclusive.')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "a755964d",
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability of {1, 6} is: 0.333\n"
     ]
    }
   ],
   "source": [
    "#assuming outcomes are equally likely\n",
    "def prob(event,sample_space):\n",
    "    return len(event)/len(sample_space)\n",
    "event={1,6}\n",
    "print(f'Probability of {event} is: {prob(event,rolling_dice):.3f}')    "
   ]
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