Question

use python3

Create a function that simulates the probabilities of the following scenarios. Then return list with corresponding probabilities.

A coin is tossed three times. What is the probability that exactly two heads occur, given that:

(a) the first outcome was a head? (b) the first outcome was a tail? (c) the first two outcomes were heads? (d) the first two outcomes were tails? (e) the first outcome was a head and the third outcome was a head?

For each scenario, calculate the true probability and ensure your estimate is within 10 percent of true probability.

import numpy as np
from math import factorial
def myfunction5():
your code here

return (a)

Answer 1

There are 3 coins and there can be 2 possible outcome of each coin H or T.
The sample space has size 2^3=8 and consists of triples(since 3 coins are tossed)
 HHH
 HHT  - exactly 2 heads
 HTH  - exactly 2 heads
 HTT
 THH  - exactly 2 heads
 THT
 TTH
 TTT


def my_function():
    result_list = []
    a = 2/8   # (a) the first outcome was a head i.e from the above sample space only HHT and HTH satisfy the condition
    b = 1/8   # (b) the first outcome was a tail i.e from the above sample space only THH satisfy the condition
    c = 1/8   # (c) the first two outcomes are heads i.e from the above sample space only HHT satisfy the condition
    d = 0 # (d)the first two outcomes are tails i.e from the above sample space no sample will have 2 heads under this condition
    e = 1/8  # (e) the first outcome was a head and the third outcome was a head i.e.from the above sample space only HTH satisfies the condition
    # add the required probabilities a,b,c,d,e to the result_list
    result_list.append(a)  
    result_list.append(b)
    result_list.append(c)
    result_list.append(d)
    result_list.append(e)
    return result_list


list_1 = my_function()    # calls the my_function() and stores the returned list into the list_1
print(list_1)    # prints list_1

SCREENSHOT OF CODE WITH OUTPUT: