Answer
$P(X\geq4)=0.004096+0.036864+0.13824=0.1792$
Work Step by Step
The solution is based on the binomial distribution:
$P(X=x)=C(n,x)*p^{x}*q^{n-x}$
If $x\geq4$, this means that x is either 4, 5 or 6, therefore we have to add the probabilities of these $x$ values.
If $p=0.4$, $n=6$, then $q=1-0.4=0.6$
By substituting into the given variables, we get:
$P(X=6)=C(6,6)*0.4^6*0.6^0=\frac{6!}{6!\times(6-6)!}*0.4^6*0.6^0=0.004096$
$P(X=5)=C(6,5)*0.4^5*0.6^1=\frac{6!}{5!\times(6-5)!}*0.4^5*0.6^1=0.036864$
$P(X=4)=C(6,4)*0.4^4*0.6^2=\frac{6!}{4!\times(6-4)!}*0.4^4*0.6^2=0.13824$
The sum of these values gives us:
$P(X\geq4)=0.004096+0.036864+0.13824=0.1792$
