Solving probability problems with MATLAB

How can I simulate this question using MATLAB?

Out of 100 apples, 10 are rotten. We randomly choose 5 apples without replacement. What is the probability that there is at least one rotten?

Answer 1

[Walter Roberson]

SampleSize = 100;
NumBad = 10;
NumTrials = 10000;
[~, randomized] = sort(rand(SampleSize, NumTrials), 1);
num_bad_in_first_five = sum(randomized(1:5,:) <= 10, 1);
bar(num_bad_in_first_five); title('number bad per trial')

counts = accumarray(num_bad_in_first_five.' + 1, 1, [6 1]);
bar(0:5, counts ./ NumTrials * 100); title('% of samples with exactly this many bad apples')

percent_with_at_least_one_bad = 100 - 100*(counts(1)/NumTrials)

percent_with_at_least_one_bad = 41.6200

[Estela]

THANK YOU! Any way to use poisscdf/binocdf/normcdf somewhere in there?

[Estela]

https://www.mathworks.com/matlabcentral/answers/1878587-tring-to-figure-out-a-simple-problem-that-uses-probability-functions?s_tid=srchtitle @Walter Roberson

Answer 2

[Paul Hoffrichter]

You can simulate this problem using a Monte Carlo Simluation.

https://www.mathworks.com/matlabcentral/answers/97605-are-there-any-examples-showing-how-to-perform-monte-carlo-simulation-in-matlab

Here's a probablity MATLAB video:

How to Make Predictions Using Monte Carlo Simulations

https://www.youtube.com/watch?v=0ikk_VEBkJw

Answer 3

[Pat Gipper]

Here is my take using a for loop. I wouldn't mind seeing how it is done without using a for loop

%% MonteCarloBadApples.m
% Author: Pat Gipper
% Out of 100 apples, 10 are rotten. We randomly choose 5 apples without
% replacement. What is the probability that there is at least one rotten?
n=10000;% Start with 10,000 trials
x=[ones(1,10),zeros(1,90)];% 1st 10 apples are rotten, remaining 90 are OK
p=0;% Accumulator
%
for i=1:n
    j=randperm(100);% Generate a random order of the indexes
    y=x(j);% Randomly scatter the 10 rotten apples in the group of 100
    z=sum(y(1:5))>0;% Is there a rotten apple in a group of 5?
    p=p+z;% Increment the Monte-Carlo count for this trial if a bad apple turned up
end
p=p/n;% Calculate the probability from the n trials

[Estela]

how would you plot the result?

[Walter Roberson]

%% MonteCarloBadApples.m
% Author: Pat Gipper
% Out of 100 apples, 10 are rotten. We randomly choose 5 apples without
% replacement. What is the probability that there is at least one rotten?
n=10000;% Start with 10,000 trials
x=[ones(1,10),zeros(1,90)];% 1st 10 apples are rotten, remaining 90 are OK
p=0;% Accumulator
%
for i=1:n
    j=randperm(100);% Generate a random order of the indexes
    y=x(j);% Randomly scatter the 10 rotten apples in the group of 100
    z=sum(y(1:5))>0;% Is there a rotten apple in a group of 5?
    p=p+z;% Increment the Monte-Carlo count for this trial if a bad apple turned up
end
p=p/n;% Calculate the probability from the n trials

whos p

  Name      Size            Bytes  Class     Attributes

  p         1x1                 8  double              

@Estela

You can see that the result is a scalar. There is nothing useful to plot about a scalar.

[Estela]

Any idea of a problem using Probability functions such as poisscdf,binocdf, normcdf example that I can plot? I am currentl ytrying to figure one out I would really appreciate the help!