Question

Five marbles are randomly selected with replacement. The probability that a black marble is chosen is 15%. What is the probability that at least 2 marbles are black?

Answer 1

this is a binomial distribution b(n,x;p) with probability of x success in n trials, p = success in each trial, q=failure in each trial
\[\large b(n,p;x)=\binom n x p^x q^{n-x},\;n=5, \; p=0.15,q=0.85; \;x=2,3,4,5\]sum of the probabilities obtained for the different values of &x&.