Financial Literacy: Probability and Coin-Toss Experiment

This text discusses the concepts of probability and coin-toss experiment in financial literacy. It explains the difference between theoretical and empirical probability and how increasing the number of data points can cause convergence between the two. The text also highlights the subjective nature of probability in winning games in a casino and its connection to individual skill level. Lastly, it shares a personal example of using empirical probability in making an investment decision and its limitations.

FINANCIAL LITERACY
PROBABILITY
STUDENT ID:
[Pick the date]

Part1: Coin-Toss Experiment
The results are summarised below.
a) The summary of the above outputs is indicated in the table below.
i) P (No head) = 8/50 = 4/25 = 0.16
ii) P(One head) = 16/50 = 8/25 = 0.32
iii) P (Two head) = 17/50 = 0.34
iv) P (Three head) = 9/50 = 0.18
b) Let H denote the event when a head appears on the toss of a coin. Let T denote the event
when a tail appears on the toss of a coin. The sample space comprises of the following 8
outcomes.
(TTT,THH,HTH, HHT, TTH,THT, HTT,HHH)

c) The theoretical probability for various events is as computed below.
i) P(No head) = 1/8 = 0.125
ii) P(one head) = 3/8 = 0.375
iii) P(two head) = 3/8 = 0.375
iv) P(three head) = 1/8 =0.125
d) It is apparent that there is some deviation between the theoretical results and the empirical
results and hence the two do not match. In order to cause convergence between the theoretical
and empirical results, it is essential to increase the number of data points recorded because as
the number of times the given experiment would be repeated, the empirical probability would
head towards the theoretical probability. This is because in lesser number of repetitions, it is
possible that a certain outcome may have disproportionate representation but in the long run,
this is highly unlikely.
PART II: Society Connection
The selected article highlights various probabilities relating to winning in different games in a
casino. For instance, the article states that probability of winning one roll in poker is 54.00
percent. This probability is subjective in nature as it is not based on past observation over
which the data has been collected. Also, it is not theoretical as it is not based on the number
of outcomes alone. This probability is slightly misleading considering the fact that winning in
poker is also dependent on the individual skill level and hence the probability is not expected
to be same for every player.
Article Link: https://www.gamblingsites.org/blog/double-your-way-million-casino/
PART III: Connection to Life
Recently, I took an investment decision to invest in a particular share in the stock market. In
order to make the decision, I relied on the concept of probability. I looked at the recent one

month performance of the stock and based on the empirical returns made by the stock and the
underlying probability of stock price increased, I decided to invest in the stock. This was an
example of using empirical probability based on the past one month performance of the
stock. It did not help me much in the decision considering the fact that stock performance in
the present does not necessarily mirror the past performance.