Week 0 : Activity 3
| Monte Carlo Simulation
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WEEK - 0
Extra Activity 3
Directive :
(i) To perform a Monte Carlo simulation and verify the computed probability.
(ii) Checking its credibility by manual calculations.
A Monte Carlo simulation is a powerful computational technique used to estimate the possible outcomes of an event that involves uncertainty. It works by repeatedly performing random sampling and calculations to build a probability distribution of the final results.
My Problem :
Consider 4 attempts of folding a crease in origami by 3 different people and the outcomes tell whether the fold is perfect, partially collapsed, or failed:
Person 1: failed, partially collapsed, failed, partially collapsed
Person 2: perfect, partially collapsed, failed, partially collapsed
Person 3: partially collapsed, perfect, partially collapsed, failed
If a person is chosen at random, and the outcome of one of his 4 attempts is noted, then calculate the probability that the folded crease is:
Perfect
Failed
Partially collapsed
Solution
The probability of a perfect fold:
p(perfect) = p(perfect from person 1) + p(perfect from person 2) + p(perfect from person 3)
p(perfect) = ( 1 / 3 ) × ( 0 / 4 ) + ( 1 / 3 ) × ( 1 / 4 ) + ( 1 / 3 × (1 / 4 ) = ( 1 / 6 ) = 0.166
The probability of a failed fold:
p(failed) = p(failed from person 1) + p(failed from person 2) + p(failed from person 3)
p(failed) = ( 1 / 3 ) × ( 2 / 4 ) + ( 1 / 3 ) × ( 1 / 4 ) + ( 1 / 3 × (1 / 4 ) = ( 1 / 3 ) = 0.333
The probability of a partially collapsed fold:
p(partially collapsed) = p(partially collapsed from person 1)+p(partially collapsed from person 2)+p(partially collapsed from person 3)
p(partially collapsed) = ( 1 / 3 ) × ( 2 / 4 ) + ( 1 / 3 ) × ( 1 / 4 ) + ( 1 / 3 × ( 2 / 4 ) = ( 1 / 2 ) = 0.5
So, the probabilities for each outcome are:
Perfect: 0.166
Failed: 0.333
Partially collapsed: 0.5
SIMULATION
https://colab.research.google.com/drive/15dsSsaGoR3OfESj9SiWMxJUVsPr-fR2B#scrollTo=2tocs29aPhDx
OUTPUT :
Probability of Perfect Fold : 0.1658 ≈ ( 0.166 | manual calculation value )
Probability of Failed Fold : 0.3375 ≈ (0.333 | manual calculation value )
Probability of Partially Collapsed Fold : 0.4967 ≈ (0.5 | manual calculation value )
VISUALISATION
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