function [PE,x]=Exercice4(p,alpha,beta,n,mc)
    x=question2(alpha,beta,p);
    PE=question3(alpha,beta,p,n,mc);
    [PEbeta,b]=question4(alpha,p,n,mc);
    plot (b,PEbeta)
    grid
    title('Variation de la probabilite P(E) en fonction de \beta.')
end

function x=question2(alpha,beta,p)
    u=random('unif',0,1);
    if u< p
        u=random('unif',0,1);
        if u<alpha
            x=1;
        else
            x=2;
        end
    else
       u=random('unif',0,1);
        if u<beta
            x=3;
        else
            x=4;
        end
    end
end

function PE=question3(alpha,beta,p,n,mc)
    for j = 1:mc
        nbr2 = 0;
        nbr4 = 0;
        for i = 1:n
            x=question2(alpha,beta,p);
            if x==2
                nbr2=nbr2+1;
            elseif x == 4
                nbr4=nbr4+1;
            end
        end
        pe(j) = nbr2/(nbr2+nbr4);
    end
    PE=mean(pe);
end


function [PE,b]=question4(alpha,p,n,mc)
    b=.2:.1:.90;
    N=length(b);
    for i=1:N
        PE(i)=question3(alpha,b(i),p,n,mc);
    end
end