4. five marbles are randomly selected with replacement. the probability that a black marble is chosen is 15%. a. what is the probability that at least 2 marbles are black?  p(at least 2 black) not multiple choice sadly

You have a 16.49% percent chance of having at least 2 black marbles.

This is an example of a binomial distribution. We have an event (drawing a black marble) that is only 15% likely. Out of 5 chances, we need to determine the likelihood that this occurs at least two time.

You can look up these values on a Binomial Distribution table.

We had to add up the percents for drawing 2, 3, 4, or 5 black marbles.

2 - 0.1382
3 - 0.0244 
4 - 0.0022
5 - 0.0001

Adding up these values gives us 0.1649.